Protecting Life and Integrity in Research Act of 2021 This bill prohibits the Department of Health and Human Services from conducting or supporting any research that involves the use of human fetal tissue from an induced abortion. The bill also prohibits soliciting or acquiring a donation of human fetal tissue from an induced abortion, other than for purposes of an autopsy or burial. The bill applies requirements on the research of transplantation of fetal tissue for therapeutic purposes to research on fetal tissue in general.