Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to incorporation by reference in the Registration Statement No. 333-215351 on Form S-8, the Registration Statement No. 333-224559 on Form S-8, and the Registration Statement No. 333-227625 on Form S-8 of CapStar Financial Holdings, Inc. of our reports dated March 4, 2022, 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, which appear in this Annual Report on Form 10-K of CapStar Financial Holdings, Inc. for the year ended December 31, 2021.

/s/ Elliott Davis, LLC

Franklin, Tennessee

March 4, 2022