Nursing Home Reform Modernization Act of 2021 This bill requires the Centers for Medicare & Medicaid Services (CMS) to establish a ranking system and related programs for Medicare skilled nursing facilities and Medicaid nursing facilities, taking into account the findings and recommendations of a specified advisory council. Specifically, the bill establishes the Advisory Council on Skilled Nursing Facility Rankings under Medicare and Nursing Facility Rankings under Medicaid. The council must study processes and make related recommendations for rankings, including with respect to appropriate metrics, data sources, and quality control. The CMS must then develop a ranking system and use the system to implement a high-rated facility program and a low-rated facility program. Facilities in the low-rated facility program are subject to progressive enforcement actions of increasing severity until they meet applicable standards; facilities in the high-rated facility program may also have their designations suspended if they fail to meet the requisite standards. The CMS must post facility designations on the Nursing Home Compare website in a specified manner. The Government Accountability Office must report on the quality of services provided by facilities and their compliance with applicable requirements, including the effectiveness of the bill's low-rated facility program.