Exhibit 5.1

May 11, 2020

TriState Capital Holdings, Inc.

One Oxford Centre, Suite 2700

Grant Street

Pittsburgh, Pennsylvania 15219

Ladies and Gentlemen:

We have acted as counsel to TriState Capital Holdings, Inc., a Pennsylvania corporation (the “Company”), in connection with the issuance and sale by the Company under the Securities Act of 1933, as amended (the “Act”), of $60,000,000 in aggregate principal amount of the 5.75% Fixed-to-Floating Rate Subordinated Notes due 2030 (the “Notes”) pursuant to Registration Statements on Form S-3, Registration Nos. 333-235713 and 333-222074, which were filed with the United States Securities and Exchange Commission (the “Commission”) on December 26, 2019 and December 15, 2017, respectively (together, the “Registration Statements”), including the related prospectus therein, (ii) a preliminary prospectus supplement dated May 5, 2020, filed with the Commission pursuant to Rule 424(b) promulgated under the Act, and (iii) a prospectus supplement dated May 6, 2020, filed with the Commission pursuant to Rule 424(b). The Notes are being sold pursuant to the underwriting agreement dated May 6, 2020, between Stephens Inc. and the Company (the “Underwriting Agreement”), and issued pursuant to the subordinated debt indenture dated as of May 11, 2020 (the “Base Indenture”), between the Company and U.S. Bank National Association, as trustee (the “Trustee”), as supplemented by the first supplemental indenture dated as of May 11, 2020, between the Company and the Trustee (together with the Base Indenture, the “Indenture”).

We have reviewed such corporate records, certificates and other documents, and such questions of law, as we have considered necessary or appropriate for the purposes of this opinion. We have assumed that all signatures are genuine, that all documents submitted to us as originals are authentic and that all copies of documents submitted to us conform to the originals. We have assumed further that the Trustee has duly authorized, executed and delivered the Indenture.

We have assumed further that (i) the Company is a corporation duly organized, validly existing and in good standing under the laws of the Commonwealth of Pennsylvania, (ii) the Company has all requisite power, authority and legal right to execute, deliver and perform its obligations under the Indenture and the Notes, (iii) the Company has duly authorized the Indenture and the Notes and (iv) insofar as the laws of the Commonwealth of Pennsylvania are concerned, the Company has duly executed and delivered the Indenture and the Notes. With respect to all matters of Pennsylvania law, we note that you are relying on an opinion of Karla Villatoro de Friedman, General Counsel and Assistant Secretary of the Company, which opinion is filed as Exhibit 5.2 to the Company’s current report on Form 8-K filed on the date hereof.

We have assumed further that the execution and delivery of the Indenture and the Notes by the Company and the performance by the Company of its obligations thereunder do not and will not violate or contravene any judgment, order, decree or permit issued by any court, arbitrator or governmental or regulatory authority, or conflict with or result in the breach of, or constitute a default under, any contract or other instrument binding on or affecting the Company or any subsidiary thereof or any of their respective properties or assets.

We have relied as to certain matters on information obtained from public officials, officers of the Company and other sources believed by us to be responsible.

Based upon the foregoing, and subject to the qualifications set forth below, we are of the opinion that when the Notes have been authenticated by the Trustee in accordance with the terms of the Indenture and delivered against payment therefor as specified in the Underwriting Agreement, the Notes will constitute the valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and other laws of general applicability relating to or affecting creditors’ rights and to general equity principles.

The foregoing opinion is subject to the qualifications that we express no opinion as to (i) waivers of defenses, subrogation and related rights, rights to trial by jury, rights to object to venue or other rights or benefits bestowed by operation of law, (ii) releases or waivers of unmatured claims or rights, (iii) provisions for liquidated damages and penalties, penalty interest and interest on interest, (iv) indemnification, contribution, exculpation or arbitration provisions or provisions for the non-survival of representations, to the extent they purport to indemnify any party against, or release or limit any party’s liability for, its own breach or failure to comply with statutory obligations, or to the extent such provisions are contrary to public policy, (v) restrictions upon transfers, pledges or assignments of a party’s rights under the Indenture and the Notes, (vi) provisions purporting to require a prevailing party in a dispute to pay attorneys’ fees and expenses, or other costs, to a non-prevailing party, (vii) provisions purporting to supersede equitable principles, including provisions requiring amendments and waivers to be in writing and provisions making notices effective even if not actually received, or (viii) provisions purporting to make a party’s determination conclusive.

We are members of the bar of the District of Columbia and the State of New York. We do not express any opinion herein on any laws other than the law of the State of New York.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Company’s current report on Form 8-K filed on the date hereof and thereby incorporated by reference into the Registration Statements. We also hereby consent to the reference to our firm under the heading “Legal Matters” in the prospectus constituting part of the Registration Statements. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission.

Very truly yours,

/s/ Covington & Burling LLP