Secure Background Checks Act of 2021 This bill extends federal restrictions on the receipt, possession, shipment, and transportation of firearms and ammunition to two new categories of persons: persons who fail to meet the minimum age requirements imposed by federal law and by the law of their resident state; and persons who are out-of-state residents and do not qualify for an exception, such as the temporary loan or rental of a firearm for lawful sporting purposes. Additionally, the bill imposes criminal penalties—a fine, a prison term of up to 10 years, or both—on an individual who ships, transports, or receives a firearm or ammunition while under indictment for a crime punishable by imprisonment for a term exceeding 1 year.