Terrorist Deportation Act of 2021 This bill establishes that aliens identified in the terrorist screening database, except for permanent residents, shall be deportable and inadmissible into the United States. The Department of Homeland Security (DHS) may temporarily waive the inadmissibility of such an alien if it is in the national security interests of the United States. DHS shall grant such a waiver only with the unanimous concurrence of the Department of Justice, the Federal Bureau of Investigation, the Office of the Director of National Intelligence, and the Department of State. An alien identified in the terrorist screening database shall be ineligible for various immigration benefits, including asylum, withholding or cancellation of removal, voluntary departure, or adjustment of status. DHS shall determine on an expedited basis the removal of an alien identified in the terrorist screening database, if the alien has not received a waiver and does not have permanent residence status. The alien shall be entitled to various protections, including the privilege of representation by counsel and judicial review.