HEARTS and Rural Relief Act This bill makes a series of changes relating to Medicare coverage and requirements, particularly with respect to military retirees. Specifically, the bill (1) exempts certain military retirees who are under 65 years of age, and who no longer receive Social Security Disability Insurance benefits, from the requirement to enroll in Medicare medical services in order to be eligible for TRICARE; (2) increases funding for the Medicare Improvement Fund; and (3) temporarily provides for Medicare coverage of certain prostate cancer DNA Specimen Provenance Assay tests. The bill also makes other changes to Medicare payment systems for certain items and services. Among other things, the bill (1) requires the Centers for Medicare & Medicaid Services (CMS) to specify the criteria used to exclude certain procedures from the list of covered surgical procedures that may be performed in an ambulatory surgical center under Medicare, and (2) extends the instruction from the CMS for contractors not to enforce the requirements for direct physician supervision of outpatient therapeutic services in critical access and small rural hospitals through 2021.