Federal Sunset Act of 2021 This bill abolishes a federal agency one year after it is reviewed by the Federal Agency Sunset Commission, established by the bill, unless the agency is reauthorized by Congress. Each agency, including each advisory committee, must be reviewed by the commission at least once every 12 years. The commission must (1) review and evaluate the efficiency and public need for each agency using specified criteria, (2) recommend whether each agency should be abolished or reorganized, and (3) report to Congress on introduced legislation that would establish a new agency or a new program. The commission shall terminate at the end of 2037. The Government Accountability Office and the Congressional Budget Office, in cooperation with the Congressional Research Service, shall prepare an inventory of federal programs to assist Congress and the commission in carrying out this bill.