Virginia Plan to Reduce Gun Violence Act of 2021 This bill makes various changes to federal firearms laws, including to expand background checks, limit handgun purchases, and extend firearms-related restrictions to new categories of persons. The bill also establishes a grant program to support the implementation of extreme risk protection order laws. Among its provisions, the bill establishes new background check requirements for firearm transfers between private parties (i.e., unlicensed individuals); generally prohibits an unlicensed person from purchasing more than one handgun in a 30-day period; establishes a grant program to help states and Indian tribes implement extreme risk protection order laws (i.e., red flag laws); generally requires gun owners to report lost or stolen firearms to law enforcement within 48 hours of discovery; makes it unlawful to recklessly leave a loaded and unsecured firearm in a manner that endangers a minor who is under 14 years of age; and extends firearms-related restrictions on the receipt, possession, shipment, or transportation of firearms and ammunition to persons convicted of a misdemeanor crime of stalking and persons who are subject to an extreme risk protection order.