Protecting Communities and Preserving the Second Amendment Act of 2021 This bill reauthorizes a grant program, requires the Department of Justice (DOJ) to take specified actions, creates new criminal offenses, and makes several other changes related to the sale, transfer, and possession of firearms. For example, the bill modifies and reauthorizes grants under the NICS (National Instant Criminal Background Check System) Improvement Amendments Act of 2007, requires DOJ to establish the Nationwide Project Exile Expansion Program to prosecute violations of federal firearms laws, establishes a task force within DOJ to investigate and prosecute cases of convicted felons and fugitives from justice who illegally attempt to purchase a firearm, removes certain restrictions on interstate firearms transactions, and creates stand-alone criminal offenses for trafficking in firearms and straw purchasing of firearms.