Put Students First Act of 2021 This bill prohibits the Department of Education (ED) from providing certain FY2021 education funds or COVID-19 (i.e., coronavirus disease 2019) relief funds to an elementary or secondary school that does not offer in-person instruction by April 30, 2021. A school must forfeit or return these funds if it does not offer in-person instruction by that date. Additionally, the bill outlines the use of forfeited and returned funds. A state may regain eligibility for these funds if it submits an implementation plan to ED that provides students with school choice options. If a state does not submit an implementation plan, then the funds must be provided as grants to states with the highest percentage of schools offering in-person instruction.