Exhibit 5.1

September 25, 2024
	Norton Rose Fulbright US LLP
	2200 Ross Avenue, Suite 3600
	Dallas, Texas 75201-7932
	United States
	Tel +1 214 855 8000
	Fax +1 214 855 8200
	nortonrosefulbright.com

Third Coast Bancshares, Inc.

20202 Highway 59 North, Suite 190

Humble, Texas 77338

Ladies and Gentlemen:

We have acted as special counsel to Third Coast Bancshares, Inc., a Texas corporation (the “Company”), in connection with the preparation of the Registration Statement on Form S-3 (the “Registration Statement”) to be filed on the date hereof by the Company with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), relating to the offer and sale from time to time pursuant to Rule 415 under the Securities Act by the securityholders named in the Registration Statement (the “Selling Securityholders”) of the following securities (collectively, the “Securities”): 69,400 shares (the “Series A Preferred Shares”) of the Company’s Series A Convertible Non-Cumulative Preferred Stock, par value $1.00 per share (“Series A Preferred Stock”); warrants to purchase up to 175,000 shares of the Company’s common stock, par value $1.00 per share (“Common Stock”) (or, at the election of the warrant holder in accordance with the terms of the Warrant Agreement (as defined below), up to 3,937 shares of the Company’s Series B Convertible Perpetual Preferred Stock, par value $1.00 per share (“Series B Preferred Stock”), or up to 175,000 shares of the Company’s non-voting common stock, par value $1.00 per share (“Non-Voting Common Stock”)), at an exercise price equal to $22.50 per share (collectively, the “Warrants”); up to 3,259,445 shares (the “Common Shares”) of Common Stock issuable upon conversion of shares of Series A Preferred Stock, Series B Preferred Stock, or Non-Voting Common Stock or upon exercise of the Warrants; up to 3,259,445 shares (the “Non-Voting Common Shares”) of Non-Voting Common Stock issuable upon conversion of shares of Series A Preferred Stock or upon exercise of the Warrants; and up to 69,400 Shares (the “Series B Preferred Shares”) of Series B Preferred Stock issuable upon conversion of shares of Series A Preferred Stock or upon exercise of the Warrants.

We also have participated in the preparation of the Prospectus (the “Prospectus”) contained in the Registration Statement to which this letter is an exhibit. The Securities may be sold or delivered from time to time as set forth in the Registration Statement, any amendment thereto, the Prospectus and supplement to the Prospectus pursuant to Rule 415 under the Act.

In rendering the opinions set forth below, we have examined and relied upon: (i) the Registration Statement, including the Prospectus; (ii) the Company’s First Amended and Restated Certificate of Formation, as amended (the “Certificate of Formation”); (iii) the Company’s First Amended and Restated Bylaws (the “Bylaws”); (iv) resolutions of the Board of Directors of the Company (the “Board”) relating to the Registration Statement; (v) resolutions of the Board relating to the Securities; (vi) the Certificate of Designation, Preferences and Rights of Series A Convertible Non-Cumulative Preferred Stock of Third Coast Bancshares, Inc., filed with the Texas Secretary of State on September 30, 2022 (the “Series A Certificate of Designation”); (vii) the Certificate of Designation, Preferences and Rights of Series B

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September 25, 2024 Page 2

Convertible Perpetual Preferred Stock of Third Coast Bancshares, Inc., filed with the Texas Secretary of State on September 30, 2022 (the “Series B Certificate of Designation”); (viii) each Warrant Agreement, dated as of September 30, 2022, by and between the Company and the Selling Securityholder named therein (each, a “Warrant Agreement”); and (ix) such certificates, statutes and other instruments and documents as we considered appropriate for purposes of the opinions expressed in this letter. In addition, we reviewed such questions of law as we considered appropriate to enable us to render the opinions expressed in this letter. As to matters of fact relevant to the opinions expressed below and as to factual matters arising in connection with our review of corporate documents, records, and other documents and writings, we have made no independent investigation of such facts, and we have relied in certain cases upon certificates and other communications of officers and employees of the Company without further investigation as to the facts set forth in such certificates and communications.

In connection with rendering the opinions expressed in this letter, we have assumed that:

(i) all information contained in all documents reviewed by us is true and correct;

(ii) all signatures on all documents examined by us are genuine and each individual who signed any of those documents had legal capacity and authority to do so;

(iii) all documents submitted to us as originals are authentic, all documents submitted to us as copies conform to the authentic originals of those documents and all documents examined by us are duly authorized, executed and delivered by the parties thereto (other than the Company);

(iv) the Certificate of Formation and Bylaws will not have been amended in any manner that would affect any legal conclusion set forth in this letter;

(v) the Registration Statement, and any amendments thereto (including post-effective amendments), will have become effective;

(vi) all Securities will be offered and sold in compliance with applicable federal and state securities laws and in the manner specified in the Registration Statement; and

(vii) with respect to Securities to be offered through an agent, underwriter or dealer or to or through a market maker, the form, terms and conditions of a definitive purchase, placement, agency, underwriting or similar agreement with respect to any Securities or, with respect to Securities to be sold by the Selling Securityholders directly to investors in privately negotiated transactions, the form, terms and conditions of such agreement with respect to such Securities, will have been duly authorized and validly executed and delivered by the parties thereto (other than the Company).

Based on the foregoing, and subject to the assumptions, qualifications, limitations and exceptions set forth herein, we are of the opinion that, (i) the Series A Preferred Shares are validly issued, fully paid, and non-assessable, (ii) the Warrants constitute valid and binding obligations of the Company, enforceable against the Company in accordance with their terms, (iii) upon the conversion of the Series A Preferred Stock, Series B Preferred Stock, and Non-Voting Common Stock and the exercise of the Warrants in accordance with the terms of the Series A Certificate of Designation, Series B Certificate of Designation, Certificate of Formation, and Warrant

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Agreement, as applicable, the related Common Shares will be validly issued, fully paid, and non-assessable, (iv) upon the conversion of the Series A Preferred Stock and the exercise of the Warrants in accordance with the terms of the Series A Certificate of Designation and Warrant Agreement, as applicable, the related Non-Voting Common Shares will be validly issued, fully paid, and non-assessable, and (v) upon the conversion of the Series A Preferred Stock and the exercise of the Warrants in accordance with the terms of the Series A Certificate of Designation and Warrant Agreement, as applicable, the related Series B Preferred Shares will be validly issued, fully paid, and non-assessable.

Our opinions in the paragraph above are subject to applicable bankruptcy, insolvency (including, without limitation, all laws relating to fraudulent transfer or conveyance), reorganization, moratorium and other similar laws relating to or affecting creditors’ rights generally and to general principles of equity or public policy (regardless of whether enforcement is sought in a proceeding in equity or at law), including, without limitation, (a) the possible unavailability of specific performance, injunctive relief or any other equitable remedy and (b) concepts of materiality, reasonableness, good faith and fair dealing, and we express no opinion herein with respect to provisions relating to severability or separability. The opinions expressed above are also subject to possible judicial action giving effect to governmental actions or foreign laws relating to or affecting creditors’ rights.

We express no opinions concerning (a) any provision that relates to severability or separability or purports to require that all amendments, supplements or waivers be in writing; or (b) the enforceability of indemnification provisions to the extent they purport to relate to liabilities resulting from or based upon negligence or any violation of federal or state securities or blue sky laws.

The foregoing opinions are limited to the Texas Business Organizations Code (including the applicable provisions of the Texas Constitution and the reported judicial decisions interpreting these laws), and we are expressing no opinion as to the applicability or effect of the laws of any other jurisdiction, domestic or foreign.

We express no opinion as to any matter other than as set forth in this letter, and no other opinion may be inferred or implied. Our opinion is given as of the date of this letter, and we undertake no, and disclaim any, obligation to advise you of any change in any matter set forth in this letter.

We hereby consent to the reference to our firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to the Registration Statement. By giving such consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations thereunder.

Very truly yours,

/s/ Norton Rose Fulbright US LLP

Norton Rose Fulbright US LLP