Rural Health Training Act of 2021 This bill requires the Health Resources and Services Administration to establish a grant program for rural hospitals, health clinics, and community health centers to provide training to employees who are nonphysician clinicians or health care support staff. As a condition of receiving grant-funded training, a trainee must continue working for the grantee for at least five years. The bill also expands the allowable uses of funding to include a trainee's childcare or transportation expenses. The Government Accountability Office must report on the impact of the grants on health care workforce retention at rural health care facilities.