Protecting Access to Post-COVID-19 Telehealth Act of 2021 This bill makes permanent several telehealth flexibilities that were initially authorized during the public health emergency relating to COVID-19 (i.e., coronavirus disease 2019), particularly with respect to Medicare coverage of telehealth services. For example, the bill permanently allows federally qualified health centers and rural health clinics to serve as the distant site (i.e., the location of the health care practitioner) for telehealth services under Medicare. Payment must be made in the same manner as for non-telehealth services, rather than in accordance with a separate methodology determined by the Centers for Medicare & Medicaid Services (CMS). The bill also permanently allows beneficiaries to receive Medicare telehealth services at any site, regardless of type or location, and grants the CMS general authority to waive any other requirements during any emergency period.