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 12, 2024, 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, 2023.

/s/ Elliott Davis, PLLC

Raleigh, North Carolina

March 12, 2024