Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the Registration Statements (Nos. 333-215351, 333-224559, and 333-227625) on Form S-8 of CapStar Financial Holdings, Inc. of our reports dated March 3, 2023, relating to our audits of the consolidated financial statements and the effectiveness of internal control over financial reporting of CapStar Financial Holdings, Inc. and subsidiary, appearing in the Annual Report on Form 10-K of CapStar Financial Holdings, Inc. for the year ended December 31, 2022.

/s/ Elliott Davis, LLC

Franklin, Tennessee

March 3, 2023