Healthcare Extension and Accessibility for Developmentally disabled and Underserved Population Act of 2021 or the HEADs UP Act of 2021 This bill authorizes the Department of Health and Human Services (HHS) to award grants to support health centers that provide services for individuals with developmental disabilities, including dental care. Grant recipients must provide specialized treatment to individuals with developmental disabilities as necessary. The bill also provides statutory authority for HHS to designate individuals with developmental disabilities as health-professional shortage population groups for the purposes of the National Health Service Corps (NHSC). The NHSC provides scholarships and student loan repayment awards to eligible providers who agree to work with designated populations or in areas that face shortages of primary care, dental care, and mental health care providers.