Prescription Drug Monitoring Act of 2021 This bill imposes, as a condition on certain federal funding for the Prescription Drug Monitoring Program (PDMP), additional notification and reporting requirements concerning prescriptions for potentially addictive drugs. States or territories that receive this funding must require prescribers to consult the PDMP before starting treatment with such drugs, and dispensers to report within 24 hours to the PDMP each time they fill a prescription for such drugs. In addition, the state agency administering a PDMP must analyze reported data for patterns of prescription drug misuse or abuse and provide certain information to prescribers, law enforcement, the public, and other states and territories.