Federal Firearms Licensee Protection Act of 2021 This bill modifies criminal penalties for an offense involving the theft of a firearm from a licensed importer, manufacturer, or dealer, or from their business premises. Specifically, the bill does the following: increases from 10 to 20 years the maximum prison term, and creates a 3- or 5-year mandatory minimum prison term for an offense that occurs during the commission of a burglary or robbery. An attempt to commit an offense is subject to the same penalties as a substantive offense.