Empowering Law Enforcement Act of 2021 This bill addresses issues relating to immigration enforcement. The bill declares that state and local law enforcement have inherent authority to investigate and arrest individuals to assist federal immigration enforcement. (Currently, state and local law enforcement may take certain immigration enforcement actions upon entering into an agreement with U.S. Immigration and Customs Enforcement.) The Department of Homeland Security (DHS) must reimburse state and local law enforcement for the costs of holding or transporting a detained alien. DHS may detain an alien beyond the removal period (generally the window in which DHS must remove an alien after a final order of removal) upon making certain certifications, such as a certification that the alien's release would threaten community safety. DHS may renew this certification every six months after giving the alien an opportunity to request reconsideration of the certification. An alien challenging such detention may only do so by filing an application for a writ of habeas corpus. Certain aliens subject to mandatory detention may be held without time limitation while removal proceedings are pending. DHS must detain an alien who is present in the United States without lawful status if the alien has been convicted for driving while intoxicated. DHS must establish a process to determine whether an alien not subject to mandatory detention and who has tried to comply with a removal order should be detained or released with conditions. The Department of Justice must include information about immigration law violations in the National Crime Information Center database.