Physician Assistant Education Public Health Initiatives Act of 2021 This bill establishes multiple grants within the Health Resources and Services Administration (HRSA) concerning clinical education and training of physician assistants. First, HRSA must award grants to physician assistant education programs to expand training at underserved sites (e.g., federally qualified health centers). HRSA must allocate 50% of the grant funds for rural sites and give priority to programs that propose expanding clinical rotations in pediatrics, women's health, or behavioral health. Second, HRSA must also award grants to physician assistant education programs for implementing telehealth curricula. Last, HRSA must award grants to qualified nonprofits and institutions of higher education for research on the use of simulation to mitigate shortages of clinical training sites and other ways to improve education and training of physician assistants.