Comprehensive TB Elimination Act of 2021 This bill reauthorizes for FY2022-FY2027 and revises the tuberculosis (TB) prevention and treatment grant program administered by the Centers for Disease Control and Prevention. The Health Resources and Services Administration may also award grants for TB prevention and treatment efforts to (1) state and local governments; (2) Indian tribes, Native Hawaiian health organizations, and related entities; and (3) community health centers and federally qualified health centers. Additionally, the Government Accountability Office must report on national TB prevention and treatment efforts.