Equity in Neuroscience and Alzheimer's Clinical Trials Act of 2021 or the ENACT Act of 2021 This bill sets out activities and requirements to increase the participation of underrepresented populations in research and clinical trials for Alzheimer's disease and related dementias. Specifically, the National Institute on Aging (NIA) must establish and provide technical assistance to Alzheimer's research centers located in areas with higher concentrations of minority groups. These centers must establish diagnostic and treatment clinics designed to serve minority, rural, and other underserved populations; operate clinical trials; and carry out public outreach to encourage members of minority populations to participate in clinical trials and research. Additionally, the NIA must disseminate information to members of minority populations about participating in clinical trials and take other actions to enhance diversity with respect to the Alzheimer's research that it conducts or supports. The bill also directs the NIA to increase diversity among Alzheimer's researchers by encouraging the participation of individuals who are from groups that are underrepresented in clinical, behavioral, and social sciences.