Immigration Detainer Enforcement Act of 2021 This bill expands statutory provisions to authorize the Department of Homeland Security (DHS) to request a law enforcement agency to detain an individual who has been arrested for violating any law (if the individual is believed to be an unlawfully present alien), where current provisions only explicitly authorize detainer requests for individuals arrested for violating controlled substances laws. The bill also modifies other related provisions. A law enforcement agency that has received a detainer request may hold the targeted individual for up to 48 hours. DHS may enter into agreements with law enforcement agencies to indemnify such agencies against claims for wrongful detention resulting from a detainer request. No provision of federal, state, or local law may restrict any government entity from (1) providing DHS with access to databases with information relating to issued detainers, or (2) holding an individual subject to a detainer. DHS shall periodically certify to Congress as to which state or local entities have not complied with a detainer request. Such entities shall be ineligible for compensation for costs related to honoring detainer requests. State and local entities that comply with DHS detainer requests shall have prioritized access to (1) certain law enforcement-related grants, and (2) certain excess federal property.