Prevention of Anti-Immigrant Violence Act of 2021 This bill provides protections for noncitizens who are victims of certain crimes. The bill expands eligibility for U visas, which are for victims of certain serious crimes or individuals who are likely helpful to law enforcement in persecuting such a crime, to include victims of hate crimes. The bill raises the annual cap on U visas to 12,000 (from 10,000) and designates the additional visas for victims of hate crimes. (Such caps apply only to the primary visa recipient, not to certain family members who may accompany the primary recipient.) A noncitizen with a pending application for certain immigration benefits, such as for a U visa or a T visa (human trafficking victim), may not be removed from the United States. A noncitizen with such a pending application may only be detained if there is clear and convincing evidence that (1) alternatives to detention would not reasonably ensure the noncitizen's appearance at removal proceedings, or (2) the noncitizen is a threat to the community. The Department of Justice may award grants to entities to assist noncitizen victims of hate crimes or to train law enforcement to identify and protect victims of anti-immigrant violence.