Pay Down, Upskill Act of 2021 This bill establishes the Pay Down or Upskill Education Benefit Program through which the Department of Education (ED) must provide an education benefit of up to $10,000 to each eligible individual. Eligible individual refers to an individual who (1) is at least 18 years old but less than 65 years old, and (2) received a certain recovery rebate in 2021. Specifically, the bill requires ED to provide an education benefit to an eligible individual to (1) repay all or part of the individual's qualifying student loans, or (2) pay all or part of the individual's qualified educational expenses (i.e., tuition and fees for an education or training program that results in a recognized postsecondary credential). ED must prescribe regulations for returning an education benefit when the individual withdraws or fails to complete enrollment for the individual's education or training program.