Exhibit 4.1

Execution

ISSUING AND PAYING

AGENCY AGREEMENT

between

TEXAS CAPITAL BANK, N.A.

as Issuer,

and

U.S. BANK NATIONAL ASSOCIATION

as Issuing and Paying Agent and Note Registrar

THIS ISSUING AND PAYING AGENCY AGREEMENT, made and dated as of January 31, 2014, between, Texas Capital Bank, N.A., a national banking association, as Issuer (the “Issuer”), and U.S. Bank National Association, as the Issuing and Paying Agent and Note Registrar (hereinafter sometimes called, in each such capacity, the “Agent”).

WHEREAS, the Issuer intends to issue and sell its 5.25% Subordinated Notes due 2026 (the “Bank Notes”), pursuant to the offering circular, dated January 28, 2014 (the “Offering Circular”);

NOW, THEREFORE, in consideration of the covenants and agreements made herein, the parties hereto agree as follows:

Section 1. Definitions. The words and terms used herein unless otherwise defined herein shall have the respective meanings assigned to such terms in the Bank Notes.

Section 2. Appointment and Acceptance. The Issuer hereby appoints U.S. Bank National Association as Issuing and Paying Agent and Note Registrar with respect to the Bank Notes, upon the terms and conditions set forth herein, and U.S. Bank National Association hereby accepts such appointment and agrees to perform all of the duties of Issuing and Paying Agent and Note Registrar in accordance with the terms of the Bank Notes and this Agreement.

Section 3. Form of Note Certificates. The Issuer shall deliver to the Agent completed Bank Notes executed by manual or facsimile signature of an officer of the Issuer duly authorized to execute the Bank Notes together with an order requesting the Agent to authenticate such Bank Notes (an “Authentication Order”). Such Bank Notes will be in such form as the Issuer shall deliver to the Agent.

Any Bank Note bearing the manual or facsimile signature of a person who is duly authorized to execute such Bank Note on the date such signature is affixed shall bind the Issuer after the completion thereof by the Agent notwithstanding that such person shall have ceased to hold his or her office on the date such Bank Note is countersigned and delivered by the Agent.

Unless the Issuer notifies the Agent to the contrary, all Bank Notes will be represented by one note certificate, hereinafter called the “Global Note.” The Global Note shall be registered in the name of a nominee of The Depository Trust Company (“DTC”), as Depositary. Beneficial interests in the Global Note will be shown on, and transfers thereof will be effected only through, records maintained by DTC and its participants.

Section 4. Certificate of Authorized Representatives of the Issuer. The Issuer shall from time to time furnish the Agent with a certificate of the Issuer certifying the incumbency and specimen signatures of representatives of the Issuer authorized to instruct the Agent regarding the completion and delivery of the Bank Notes (each, an “Authorized Representative”). The Agent shall have no responsibility to the Issuer to determine whether a signature of an Authorized Representative is genuine if such signature resembles the specimen signature of such Authorized Representative on such certificate.

Section 5. Duties of Issuing Agent: Completion, Authentication and Delivery.

(a) The Global Note shall be issued and delivered in accordance with the Blanket Letter of Representations from the Issuer to DTC dated as of January 30, 2014. All instructions regarding the completion and delivery of the Global Note shall be given by an Authorized Representative by facsimile or other means acceptable to the Agent. All Authentication Orders with respect to the completed Global Note delivered for authentication to the Agent shall be in writing and shall be executed by an Authorized Representative. Upon receipt of instructions as described above, the Agent shall:

(1) manually countersign the Global Note by any one of the officers or employees of the Agent duly authorized and designated by it for such purpose; and

(2) deliver the Global Note to DTC or hold on behalf of DTC pursuant to DTC’s instructions.

(b) The Agent shall incur no liability to the Issuer in acting hereunder upon any instructions or Authentication Order contemplated hereby which the Agent believed in good faith to have been given by an Authorized Representative.

(c) Each instruction or Authentication Order given to the Agent in accordance with this Section 5 shall constitute a representation and warranty to the Agent by the Issuer that the issuance and delivery of the Bank Note or Notes to which the instruction or Authentication Order relates have been duly and validly authorized by the Issuer, that such Bank Note or Notes when completed, countersigned and delivered pursuant hereto, will constitute the legal, valid and binding obligations of the Issuer, and that the Agent’s appointment to act for the Issuer hereunder has been duly authorized by all necessary corporate action of the Issuer.

Section 6. Duties of Note Registrar: Registration, Registration of Transfer and Exchange. The Agent, in its capacity as Note Registrar, shall, so long as any of the Bank Notes remain outstanding, subject without limitation to Section 3 above, maintain all records as may be customary or provided to it, including all forms of transfer, probates, letters of administration and powers of attorney, and shall:

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(a) Keep at its Paying Agent Office in Dallas, Texas (the “Paying Agent Office”), a register (the “Note Register”) in such form as the Agent may determine, in which, subject to reasonable regulations as it may prescribe, it shall provide for the registration of Bank Notes and of transfers of Bank Notes;

(b) Maintain records showing for each outstanding Bank Note the principal amount and other terms thereof; all subsequent transfers and changes of ownership thereof; and the name, address and tax identification number of the registered holder of such Bank Note (each, a “Holder”);

(c) Record any transfer of Bank Notes which it believes in good faith to have been duly authorized; provided that, the Agent may refuse to record any transfer of the Bank Notes if in good faith the Agent deems such refusal necessary in order to avoid any liability either to the Issuer or to itself;

(d) Prepare all such lists of Holders as may be required by the Issuer or any person needing such information and so authorized in writing by the Issuer; and

(e) During regular office hours and upon reasonable prior written notice, make the Note Register available to the Issuer or any person needing such information and so authorized in writing by the Issuer for inspection and for the taking of copies thereof; provided that the Agent shall have no responsibility or liability for any aspect of the records relating to or payments made on account of beneficial ownership interests in the Global Note or for maintaining, supervising or reviewing any records relating to such beneficial ownership interests, and it shall be fully protected in acting or refraining from acting on any such information provided by DTC.

Upon surrender for registration of transfer of any Bank Note at the Paying Agent Office, the Issuer shall execute, and the Agent shall authenticate and deliver, in the name of the designated transferee or transferees, one or more new Bank Notes of authorized denominations (which in no case may be less than $250,000 and integral multiples of $1,000 in excess thereof) and of a like tenor and aggregate principal amount; provided that, unless and until it is exchanged in whole or in part for individual Bank Notes represented thereby, the Global Note may not be transferred except as a whole by DTC to a nominee of DTC, or by a nominee of DTC to DTC or another nominee of DTC, or by DTC or any such nominee to a successor depositary or a nominee of such successor depositary.

If (i) DTC notifies the Issuer in writing that it is unwilling or unable to act as Depositary or DTC ceases to be a clearing agency registered under the Securities Exchange Act of 1934, as amended, and a successor depositary is not appointed by the Issuer within 90 days, (ii) the Issuer, at its option, notifies the Agent in writing that it elects to cause the issuance of Bank Notes in definitive form or (iii) any event shall have happened and be continuing that, after notice or lapse of time or both, would constitute an Event of Default with respect to the Bank Notes, then, upon surrender by DTC or a successor depositary of the Global Notes, the Agent

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shall authenticate and deliver Bank Notes, upon receipt of instructions from the Issuer, of like tenor and terms in definitive form in an aggregate principal amount equal to the principal amount of the Global Note outstanding in exchange for such Global Note, to each person that DTC or a successor depositary identifies as the beneficial owner of the related Bank Notes.

Upon the exchange of the Global Note for Bank Notes in definitive form upon the occurrence of any of the events described above, the Global Note shall be cancelled by the Agent. Bank Notes issued in exchange for the Global Note shall be registered in such names and in such authorized denominations, and delivered to such addresses, as DTC, pursuant to instructions from its direct or indirect participants or otherwise, shall instruct the Agent in writing. The Agent shall deliver such Bank Notes to the persons in whose names such Bank Notes are registered or to DTC, in fully registered form without coupons in denominations of $250,000 or any amount in excess thereof that is an integral multiple of $1,000. Such Bank Notes may not subsequently be exchanged by a Holder for Bank Notes in denominations of less than $250,000.

In case any Bank Note shall at any time become mutilated, destroyed, lost or stolen and such Bank Note or evidence satisfactory to the Issuer of the loss, theft or destruction thereof (together with indemnity satisfactory to the Agent and the Issuer and such other documents or proof as may be required by the Agent and the Issuer) shall be delivered to the Agent and the Issuer, the Agent shall authenticate and deliver, upon receipt of instructions from the Issuer, a new Bank Note of like tenor in exchange for the Bank Note so mutilated, or in lieu of the Bank Note so destroyed or lost or stolen.

Section 7. Duties of Paying Agent: Payment of Bank Notes. Payment of principal (and premium, if any) and interest on the Bank Notes shall be made by the Agent in the manner and on the dates specified in the Bank Notes from funds deposited by the Issuer with the Agent for such payments as provided in Section 8. The Agent shall have no obligation to use its own funds for any such payment of principal, premium or interest on the Bank Notes. Payments due at the maturity or redemption of a Bank Note shall be made only upon presentation and surrender of such Bank Note. Any money that the Issuer pays to the Agent for the purpose of making payments on the Bank Notes and that remains unclaimed two years after the payments were due will, at the Issuer’s request, be returned to it. After that time any Holders of such Bank Notes can only look to the Issuer for payment on such Bank Notes.

Section 8. Deposit of Funds. The Issuer shall deposit with the Agent by 9:30 a.m., New York time (i) on each Interest Payment Date (as such term is defined in such Bank Note) of a Bank Note an amount in immediately available funds sufficient to pay the interest due on such date and (ii) on the Maturity Date (as such term is defined in such Bank Note) or earlier redemption date an amount in immediately available funds sufficient to pay the principal of such Bank Note, the premium due thereon, if any, and the interest accrued thereon to such Maturity Date or redemption date, as the case may be. The Agent shall clearly identify in its books and records funds relating to the Bank Notes. At the Issuer’s request, any money that the Issuer pays to the Agent for the purpose of making payments on Bank Notes and that remains unclaimed two years after the payments were due shall be returned to the Issuer (after which time a Holder may only look to the Issuer for payment on Bank Notes).

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Section 9. Fees and Expenses of the Agent. The Issuer shall pay such fees and expenses of the Agent for the performance of its duties as Issuing and Paying Agent and Note Registrar hereunder as may be mutually agreed upon from time to time in writing.

Section 10. Conditions. The Agent accepts its obligations herein set forth upon the terms and conditions hereof, including the following, to all of which the Issuer agrees:

Section 11. Indemnification. Notwithstanding any satisfaction or discharge of any Bank Notes, the Issuer shall indemnify the Agent and its directors, officers, agents and employees against any and all loss, liability, costs, damages, claims, actions, expenses or demands which it may incur or sustain or which may be made against it in connection with its appointment or the exercise of its powers and duties hereunder as well as the reasonable costs, including the expenses and fees of counsel in defending any claim, action or demand, except such as may result from the willful misconduct, gross negligence, bad faith or reckless disregard by the Agent or any of its officers, employees or agents of any of the Agent’s duties, responsibilities or obligations under this Agreement. The Agent shall incur no liability and shall be indemnified and held harmless by the Issuer for, or in respect of, any actions taken or suffered to be taken in good faith by the Agent in accordance herewith and in reliance upon the written opinion or advice of counsel or (ii) written instructions that, after reasonable investigation, are believed to be duly authorized by the Issuer.

Section 12. Resignation or Removal of the Agent.

(a) Except as provided below, the Agent may at any time resign as Note Registrar, as Issuing Agent or as Paying Agent by giving written notice to the Issuer of its intention to resign from any or all such offices, specifying the date on which its desired resignation shall become effective; provided that such notice shall be given not less than 45 days prior to the said effective date unless the Issuer otherwise agrees in writing. Except as provided below, the Agent may be removed from any or all of the offices to which it is hereby appointed by the Issuer delivering to the Agent an instrument in writing signed by the Issuer specifying such removal and the date when it shall become effective (such effective date being at least 20 days after said filing).

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(b) If at any time the Agent shall resign or be removed from any or all of the offices to which it is hereby appointed, then a successor Note Registrar, Issuing Agent or Paying Agent, as the case may be, shall be appointed by the Issuer by an instrument in writing delivered to the successor Note Registrar, Issuing Agent or Paying Agent, as the case may be. Upon the appointment as aforesaid of a successor Note Registrar, Issuing Agent or Paying Agent, as the case may be, and acceptance by the latter of such appointment, the former Note Registrar, Issuing Agent or Paying Agent, as the case may be, shall cease to hold such office.

(c) Any successor Note Registrar, Issuing Agent or Paying Agent appointed hereunder shall execute and deliver to its predecessor and the Issuer an instrument accepting such appointment hereunder, and thereupon such successor Note Registrar, Issuing Agent or Paying Agent, without any further act, deed or conveyance, shall become vested with all the authority, rights, powers, immunities, duties and obligations of such predecessor with like effect as if originally named as the Note Registrar, Issuing Agent or Paying Agent hereunder, and such predecessor shall thereupon become obligated to transfer and deliver, and such successor shall be entitled to receive, copies of any relevant records maintained by such predecessor Note Registrar, Issuing Agent or Paying Agent.

(d) Any corporation into which the Agent may be merged or converted or any corporation with which the Agent may be consolidated or any corporation resulting from any merger, conversion or consolidation to which the Agent shall be a party shall, to the extent permitted by applicable law, be the successor Note Registrar, Issuing Agent or Paying Agent under this Agreement without the execution or filing of any paper or any further act on the part of any of the parties hereto. Notice of any such merger, conversion or consolidation shall forthwith be given to the Issuer.

(e) The provisions of Section 11 hereof shall survive any resignation or removal hereunder and the termination of this Agreement with respect to matters occurring prior to any such resignation or removal and the termination of this Agreement.

Section 13. Event of Default Notification. The Issuer will promptly notify the Agent upon the occurrence of an Event of Default or of the curing of an Event of Default, and the Issuer will provide copies of any such notice of the occurrence of an Event of Default or the curing of an Event of Default to the Agent, whereupon the Agent will promptly mail by first-class mail, postage prepaid, copies of such notice to the Holders of the Bank Notes in the Note Register at their respective addresses appearing in the Agent’s records.

Section 14. Notices. All notices, instructions and communications between the parties hereto in connection with this Agreement shall be delivered in person, sent by letter, facsimile or communicated by telephone (subject, in the case of communication by telephone, to written confirmation dispatched within two Business Days by letter or facsimile), in the case of the Issuer, to it at 2000 McKinney Avenue, Suite 700, Dallas, Texas 75201, Attention: Peter B. Bartholow, with a copy to Bracewell & Giuliani LLP, 1445 Ross Avenue, Suite 3800, Dallas, Texas 75202-2711, Attention: Michael W. Tankersley, and in the case of the Agent, to it at 13737 Noel Road, Suite 800, Dallas, Texas 75240, Attention: Global Corporate Trust Services.

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Section 15. Successors and Assigns. The rights, duties and obligations of the Issuer and the Agent hereunder shall inure, without further act, to their respective successors and assigns.

Section 16. Amendments. This Agreement may be amended only by an instrument in writing signed by the Issuer and the Agent.

Section 17. Counterparts. This Agreement may be executed in one or more counterparts and, if executed in one or more counterparts, the executed counterparts shall each be deemed to be an original but all such counterparts shall together constitute one and the same instrument.

Section 18. GOVERNING LAW. THIS AGREEMENT SHALL BE GOVERNED BY, AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

[signature page follows]

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be executed as of the day and year first above written.

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