Gym Mitigation and Survival Act of 2021 or the GYMS Act of 2021 This bill establishes a grant program to provide economic support to eligible fitness facilities in response to the COVID-19 (i.e., coronavirus disease 2019) pandemic. Specifically, the bill authorizes the Small Business Administration to make initial and supplemental grants to privately owned fitness facilities that primarily provide health or fitness services and that do not offer golf, hunting, sailing, or riding facilities. The total amount of grant funds for a recipient may not exceed $25 million, and the recipient must use these funds for payroll costs, rent or mortgage obligations, and other ordinary and necessary business expenses.