Federal Agency Sunset Commission Act of 2021 This bill provides for the establishment of the Federal Agency Sunset Commission to submit to Congress a schedule for review and abolishment of each agency, including each advisory committee. The schedule for review shall be in the form of a joint resolution. Each agency shall be abolished unless reauthorized by Congress. For each agency, the commission must schedule a date of abolishment to occur 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) analyze the authority claimed by the executive branch but not specifically authorized by statute; (3) recommend whether each agency should be abolished, reorganized, or continued; and (4) report to Congress on introduced legislation that would establish a new agency or a new program. 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. The bill provides for expedited consideration of the schedule for review and abolishment.