Exhibit 10.13

HESS MIDSTREAM PARTNERS

LONG-TERM INCENTIVE PLAN

PHANTOM UNIT AGREEMENT

Pursuant to this Phantom Unit Agreement, dated as of the Grant Date set forth in the Grant Notice below (this “Agreement”), Hess Midstream Partners GP LLC (the “Company”), as the general partner of Hess Midstream Partners LP (the “Partnership”), hereby grants to the individual identified in the Grant Notice below (the “Participant”) the following Award of Phantom Units (“Phantom Units”), pursuant and subject to the terms and conditions of this Agreement and the Hess Midstream Partners LP 2015 Long-Term Incentive Plan, as amended from time to time (the “Plan”), the terms and conditions of which are hereby incorporated into this Agreement by reference. Each Phantom Unit granted hereunder shall constitute a Phantom Unit under the terms of the Plan and is hereby granted in tandem with a corresponding DER, as further detailed in Section 3 below. In the event of any conflict between the terms of this Agreement and the Plan, the terms of the Plan shall control. Except as otherwise expressly provided herein, all capitalized terms used in this Agreement, but not defined herein, shall have the meanings provided in the Plan.

GRANT NOTICE

Subject to the terms and conditions of this Agreement, the principal features of this Award are as follows:

Participant: [            ]

Number of Phantom Units: [        ] Phantom Units

Grant Date: [                    ], 20[    ]

Vesting of Phantom Units: [To be provided in individual agreements]; provided that the Phantom Units shall be subject to accelerated vesting in certain circumstances as set forth in Section 4.

Forfeiture of Phantom Units: In the event of a termination of the Participant’s Service for any reason, all Phantom Units that have not vested prior to or in connection with such termination of Service shall thereupon automatically be forfeited by the Participant without further action and for no consideration.

Payment of Phantom Units: Vested Phantom Units shall be paid to the Participant in the form of Units as set forth in and subject to Section 5 below.

DERs: Each Phantom Unit granted under this Agreement shall be issued in tandem with a corresponding DER each of which shall entitle the Participant to receive payments in an amount equal to Partnership distributions with respect to a Unit in accordance with Section 3 below.

TERMS AND CONDITIONS OF PHANTOM UNITS

1. Grant. The Company hereby grants to the Participant, as of the Grant Date, an Award of the number of Phantom Units set forth in the Grant Notice above, subject to all of the terms and conditions contained in this Agreement and the Plan.

2. Phantom Units. Subject to Section 4 below, each Phantom Unit that vests shall represent the right to receive payment, in accordance with Section 5 below, in the form of one (1) Unit. Unless and until a Phantom Unit vests, the Participant will have no right to payment in respect of such Phantom Unit. Prior to actual payment in respect of any vested Phantom Unit, such Phantom Unit will represent an unsecured obligation of the Company, payable (if at all) only from the general assets of the Company.

3. Grant of Tandem DER. Each Phantom Unit granted hereunder is hereby granted in tandem with a corresponding DER, which shall remain outstanding from the Grant Date until the earlier of the payment or forfeiture of the related Phantom Unit, and which shall be subject to all of the terms and conditions contained in this Agreement and the Plan. Each vested DER shall entitle the Participant to receive payments, subject to and in accordance with this Agreement, in an amount equal to any distributions made by the Partnership following the Grant Date in respect of the Unit underlying the Phantom Unit to which such DER relates. The Company shall establish, with respect to each Phantom Unit, a separate DER bookkeeping account for such Phantom Unit (a “DER Account”), which shall be credited (without interest) on the applicable distribution dates with a notional amount equal to any distributions made by the Partnership during the period that such Phantom Unit remains outstanding with respect to the Unit underlying the Phantom Unit to which such DER relates. Upon the vesting of a Phantom Unit, the DER (and the DER Account) with respect to such vested Phantom Unit shall also become vested. The DER corresponding to a Phantom Unit shall expire upon the settlement of that Phantom Unit. Similarly, upon the forfeiture of a Phantom Unit, the DER (and the DER Account) with respect to such forfeited Phantom Unit shall also be forfeited without payment of consideration.

4. Vesting and Forfeiture.

(a) Vesting. Subject to Section 4(c) below, the Phantom Units shall vest in such amounts and at such times as are set forth in the Grant Notice above.

(b) Accelerated Vesting. [To be provided in individual agreements].

(c) Forfeiture. In the event of a termination of the Participant’s Service for any reason, all Phantom Units that have not vested prior to or in connection with such termination of Service shall thereupon automatically be forfeited by the Participant without further action and without payment of consideration therefor. No portion of the Phantom Units which has not become vested at the date of the Participant’s termination of Service shall thereafter become vested.

(d) Payment. Vested Phantom Units shall be subject to the payment provisions set forth in Section 5 below.

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5. Payment of Phantom Units and DERs.

(a) Phantom Units. Unpaid, vested Phantom Units shall be paid to the Participant in the form of Units in a lump-sum as soon as reasonably practical, but not later than sixty (60) days following the date on which such Phantom Units vest. Payments of any Phantom Units that vest in accordance herewith shall be made to the Participant (or in the event of the Participant’s death, to the Participant’s estate) in whole Units in accordance with this Section 5. In lieu of the foregoing, the Committee may elect at its discretion to pay some or all of the Phantom Units in cash equal to the Fair Market Value of the Units that would otherwise be distributed as of the date of vesting.

(b) DERs. Unpaid, vested DERs shall be paid to the Participant as follows: as soon as reasonably practical, but not later than sixty (60) days, following the date on which a Phantom Unit and related DER vests, the Participant shall be paid an amount in cash equal to the amount then credited to the DER Account maintained with respect to such Phantom Unit.

(c) Potential Delay. Notwithstanding anything to the contrary in this Agreement, no amounts payable under this Agreement shall be paid to the Participant prior to the expiration of the six (6)-month period following his “separation from service” (within the meaning of Treasury Regulation Section 1.409A-1(h)) (a “Separation from Service”) to the extent that the Company determines that paying such amounts prior to the expiration of such six (6)-month period would result in a prohibited distribution under Section 409A(a)(2)(B)(i) of the Code. If the payment of any such amounts is delayed as a result of the previous sentence, then on the first business day following the end of the applicable six (6)-month period (or such earlier date upon which such amounts can be paid under Section 409A of the Code without resulting in a prohibited distribution, including as a result of the Participant’s death), such amounts shall be paid to the Participant.

6. Tax Withholding. Unless other arrangements have been made that are acceptable to the Company in its sole discretion, the Company or any Affiliate thereof is authorized to deduct or withhold, or cause to be deducted or withheld, (i) from any Award, (ii) from any payment due or transfer made under any Award or (iii) from any compensation or other amount owing to a Participant the amount of any applicable taxes required to be withheld by the Company or any Affiliate in respect of an Award, including taxes required to be withheld in connection with its grant, its exercise, the lapse of restrictions thereon or any payment or transfer thereunder or under the Plan, and to take such other action as may be necessary in the opinion of the Company to satisfy its withholding obligations for the payment of such taxes. The Company or any Affiliate may withhold cash or Units, including Units that would otherwise be issued pursuant to such Award or other property. In the event that Units that would otherwise be issued pursuant to an Award are used to satisfy such withholding obligations, the number of Units so withheld or surrendered shall be limited to the number of Units that have a Fair Market Value on the date of withholding equal to the aggregate amount of the Company’s or any Affiliate’s withholding obligation based on the minimum applicable statutory withholding rates for federal, state, local and foreign income tax and payroll tax purposes.

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7. Rights as Unit Holder. Neither the Participant nor any person claiming under or through the Participant shall have any of the rights or privileges of a holder of Units in respect of any Units that may become deliverable hereunder unless and until certificates representing such Units shall have been issued or recorded in book entry form on the records of the Partnership or its transfer agents or registrars, and delivered in certificate or book entry form to the Participant or any person claiming under or through the Participant.

8. Transferability of Units. Neither the Phantom Units nor any right of the Participant under the Phantom Units (including any DER) may be assigned, alienated, pledged, attached, sold or otherwise transferred or encumbered by the Participant (or any permitted transferee) other than by will or the laws of descent and distribution and any such purported assignment, alienation, pledge, attachment, sale, transfer or encumbrance shall be void and unenforceable against the Company, the Partnership and any of their Affiliates. Notwithstanding the foregoing, the Participant may designate the beneficiary or beneficiaries to receive the Phantom Units or other amounts which may be delivered in respect of this Award after the Participant’s death. Such designation may be made by the Participant on the enclosed beneficiary designation form and (unless the Participant has waived such right) may be changed by the Participant from time to time by filing a new beneficiary designation form with the Committee. If the Participant does not designate a beneficiary or if no designated beneficiary(ies) survives the Participant, the Participant’s beneficiary will be the legal representative of the Participant’s estate.

9. Distribution of Units. Unless otherwise determined by the Committee or required by any applicable law, rule or regulation, neither the Company nor the Partnership shall deliver to the Participant certificates evidencing Units issued pursuant to this Agreement and instead such Units shall be recorded in the books of the Partnership (or, as applicable, its transfer agent or equity plan administrator). All certificates for Units issued pursuant to this Agreement and all Units issued pursuant to book entry procedures hereunder shall be subject to such stop transfer orders and other restrictions as the Company may deem advisable under the Plan or the rules, regulations, and other requirements of the SEC, any stock exchange upon which such Units are then listed, and any applicable federal or state laws, and the Company may cause a legend or legends to be inscribed on any such certificates or book entry to make appropriate reference to such restrictions. In addition to the terms and conditions provided herein, the Company may require that the Participant make such covenants, agreements, and representations as the Company, in its sole discretion, deems advisable in order to comply with any such laws, regulations, or requirements. No fractional Units shall be issued or delivered pursuant to the Phantom Units and the Committee shall determine, in its discretion, whether cash, other securities, or other property shall be paid or transferred in lieu of fractional Units or whether such fractional Units or any rights thereto shall be canceled, terminated, or otherwise eliminated.

10. Partnership Agreement. Units issued upon payment of the Phantom Units shall be subject to the terms of the Plan and the Partnership Agreement. Upon the issuance of Units to the Participant, the Participant shall, automatically and without further action on his or her part, (i) be admitted to the Partnership as a Limited Partner (as defined in the Partnership Agreement) with respect to the Units, and (ii) become bound, and be deemed to have agreed to be bound, by the terms of the Partnership Agreement.

11. No Effect on Service. Nothing herein or in the Plan will be construed as conferring on the Participant or anyone else the right to continue in the employ or service of the Company or any Affiliate thereof. Furthermore, the Company and its Affiliates may at any time dismiss the Participant from employment or consulting free from any liability or

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any claim under the Plan or this Agreement, unless otherwise expressly provided in the Plan, this Agreement or any other written agreement between the Participant and the Company or an Affiliate thereof.

12. Terms of Employment. The Plan is a discretionary plan. The Participant hereby acknowledges that neither the Plan nor this Agreement forms part of the Participant’s terms of Service and nothing in the Plan may be construed as imposing on the Company, the Partnership or any of their Affiliates a contractual obligation to offer participation in the Plan to any Employee, Consultant or Director. The Company, the Partnership and their Affiliates are under no obligation to grant further Phantom Units to the Participant under the Plan or, if such Phantom Units are granted, to grant such Award on the same or similar terms as provided in this Agreement. If the Participant ceases to be an Employee, Consultant or Director for any reason, the Participant shall not be entitled by way of compensation for loss of office or otherwise howsoever to any sum or other benefit to compensate the Participant for the loss of any rights under this Agreement or the Plan.

13. Severability. The invalidity or unenforceability of any provision of this Agreement in any jurisdiction will not affect the validity, legality or enforceability of the remainder of this Agreement in such jurisdiction or the validity, legality or enforceability of any provision of this Agreement in any other jurisdiction, it being intended that all rights and obligations of the parties hereunder will be enforceable to the fullest extent permitted by law.

14. No Guarantee of Tax Consequences. None of the Board, the Committee, the Company or the Partnership provides or has provided any tax advice to the Participant or makes or has made any assurance, commitment or guarantee to the Participant that any federal, state, local or other tax treatment will (or will not apply) or be available to the Participant with respect to the issuance, holding, vesting, payment, settlement or other occurrence with respect to the Phantom Units, the DERs, the Units or the transactions contemplated by this Agreement. The Participant represents that he or she is in no manner relying on such entities or their representatives for tax advice or an assessment of such tax consequences, and such entities assume no liability with respect to any tax or associated liabilities to which the Participant may be subject. The Participant understands that the Participant may suffer adverse tax consequences in connection with the Phantom Units and DERs granted pursuant to this Agreement.

15. Entire Agreement; Amendments, Suspension and Termination. This Agreement (including the Plan which is incorporated herein by reference) contains the entire agreement between the parties hereto with respect to the subject matter contained herein, and supersedes all prior agreements or prior understandings, whether written or oral, between the parties hereto relating to such subject matter. To the extent permitted by the Plan, this Agreement may be wholly or partially amended or otherwise modified, suspended or terminated at any time or from time to time by the Board or the Committee. Except as provided in the preceding sentence, this Agreement cannot be modified, altered or amended, except by an agreement, in writing, signed by both the Partnership and the Participant.

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16. Notices. Any notice which may be required or permitted under this Agreement will be in writing and will be delivered in person, or via facsimile transmission, overnight courier service or certified mail, return receipt requested, postage prepaid, properly addressed as follows:

(a) If the notice is to the Company, the Partnership or any of their Affiliates, to the attention of the Secretary of Hess Corporation, 1185 Avenue of the Americas, New York, New York 10036, or at such other address as the Company, the Partnership or any of their Affiliates by notice to the Participant may designate in writing from time to time.

(b) If the notice is to the Participant, at the Participant’s address as shown on the records of the Company, the Partnership or their Affiliates, or at such other address as the Participant, by notice to the Company, the Partnership or their Affiliates, may designate in writing from time to time.

17. Lock-Up Agreement. The Participant shall agree, if so requested by the Company or the Partnership and any underwriter in connection with any public offering of securities of the Partnership or any Affiliate thereof, not to directly or indirectly offer, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant for the sale of or otherwise dispose of or transfer any Units held by him or her for such period, not to exceed one hundred eighty (180) days following the effective date of the relevant registration statement filed under the Securities Act in connection with such public offering, as such underwriter shall specify reasonably and in good faith. The Company or the Partnership may impose stop-transfer instructions with respect to securities subject to the foregoing restrictions until the end of such 180-day period. Notwithstanding the foregoing, the 180-day period may be extended in the discretion of the Company for up to such number of additional days as is deemed necessary by such underwriter or the Company or Partnership to continue coverage by research analysts in accordance with FINRA Rule 2711 or any successor or other applicable rule.

18. Compliance with Laws. The Participant acknowledges that the Plan and this Agreement are intended to conform to the extent necessary with all provisions of the Securities Act and the Exchange Act, any and all regulations and rules promulgated by the SEC thereunder, all applicable state securities laws and regulations, and any other law, rule or regulation applicable thereto. Notwithstanding anything herein to the contrary, the Plan shall be administered, and the Phantom Units and DERs are granted, only in such a manner as to conform to such laws, rules and regulations. To the extent permitted by applicable law, the Plan and this Agreement shall be deemed amended to the extent necessary to conform to such laws, rules and regulations.

19. Code Section 409A. The intent of the parties is that the payments and benefits under this Agreement comply with or be exempt from Section 409A of the Code and, accordingly, to the maximum extent permitted, this Agreement shall be interpreted to be in compliance therewith. Nevertheless, to the extent that the Committee determines that the Phantom Units or DERs may not be exempt from (or compliant with) Section 409A of the Code, the Committee may (but shall not be required to) amend this Agreement in a manner intended to comply with the requirements of Section 409A of the Code or an exemption therefrom (including amendments with retroactive effect), or take any other actions as it deems necessary or appropriate to attempt to (a) exempt the Phantom Units or DERs from Section 409A of the Code and/or preserve the intended tax treatment of the benefits provided with respect to the Phantom Units or DERs, or (b) comply with the requirements of Section 409A of the Code. To the extent applicable, this Agreement shall be interpreted in accordance with the provisions of Section 409A of the Code. Notwithstanding anything in this Agreement to the contrary, to the extent that any payment or benefit hereunder constitutes non-exempt “nonqualified deferred compensation” for purposes of Section 409A

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of the Code, and such payment or benefit would otherwise be payable or distributable hereunder by reason of the Participant’s termination of Service, all references to the Participant’s termination of Service shall be construed to mean a Separation from Service, and the Participant shall not be considered to have a termination of Service unless such termination constitutes a Separation from Service with respect to the Participant.

20. Adjustments; Clawback. The Participant acknowledges that the Phantom Units are subject to modification and forfeiture in certain events as provided in this Agreement and Section 7 of the Plan. The Participant further acknowledges that the Phantom Units, DERs and Units issuable hereunder, whether vested or unvested and whether or not previously issued, are subject to clawback as provided in Section 8(o) of the Plan.

21. Successors and Assigns. The Company or the Partnership may assign any of its rights under this Agreement to single or multiple assignees, and this Agreement shall inure to the benefit of the successors and assigns of the Company and the Partnership. Subject to the restrictions on transfer contained herein, this Agreement shall be binding upon the Participant and his or her heirs, executors, administrators, successors and assigns.

22. Further Assurances. Each party hereto will do and perform (or will cause to be done and performed) all such further acts and shall execute and deliver all such other agreements, certificates, instruments and documents as any other party hereto reasonably may request in order to carry out the intent and accomplish the purposes of this Agreement and the Plan and the consummation of the transactions contemplated thereunder.

23. Governing Law. The validity, construction, and effect of this Agreement and any rules and regulations relating to this Agreement shall be determined in accordance with the laws of the State of Delaware without regard to its conflicts of laws principles.

24. Counterparts; Headings. This Agreement may be executed in one or more counterparts, each of which will be deemed to be an original, but all of which will constitute one and the same instrument. Headings are given to the sections and subsections of this Agreement solely as a convenience to facilitate reference. Such headings shall not be deemed in any way material or relevant to the construction or interpretation of this Agreement or any provision hereof.

25. Data Protection. By signing this Agreement, the Participant consents to the holding and processing of personal data provided by the Participant to the Company, the Partnership or their Affiliates for all purposes necessary for the operation of the Plan. These include, but are not limited to:

(a) Administering and maintaining the Participant’s records;

(b) Providing information to any registrars, brokers or third party administrators of the Plan; and

(c) Providing information to future purchasers of the Company or any Affiliate in which the Participant works.

[Signature page follows]

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The Participant’s signature below indicates the Participant’s agreement with and understanding that this Award is subject to all of the terms and conditions contained in the Plan and in this Agreement, and that, in the event that there are any inconsistencies between the terms of the Plan and the terms of this Agreement, the terms of the Plan shall control. The Participant further acknowledges that the Participant has read and understands the Plan and this Agreement, which contains the specific terms and conditions of this grant of Phantom Units and DERs. The Participant hereby agrees to accept as binding, conclusive and final all decisions or interpretations of the Committee upon any questions arising under the Plan or this Agreement.

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