Protecting Domestic Violence and Stalking Victims Act of 2021 This bill establishes new federal firearms restrictions for individuals who are convicted of misdemeanor stalking offenses. The bill expands the categories of persons who are prohibited from receiving, possessing, shipping, or transporting a firearm or ammunition. Specifically, it adds a new category of prohibited persons: persons convicted of a misdemeanor crime of stalking. The term misdemeanor crime of stalking means a misdemeanor stalking offense under federal, state, tribal, or municipal law and a course of harassment, intimidation, or surveillance of another person that (1) places such person in reasonable fear of harm to themselves, an immediate family member, a household member, or a spouse or intimate partner (including a current or former dating partner); or (2) causes emotional distress to such person. The bill also specifically prohibits dating partners who are convicted of a misdemeanor crime of domestic violence or who are subject to certain restraining orders from receiving, possessing, shipping, or transporting a firearm or ammunition. Currently, such restrictions generally only apply to spouses, co-parents, and cohabitants.