Living Donor Protection Act of 2021 This bill prohibits certain insurance carriers from discriminating against, and provides other protections for, living organ donors. Specifically, carriers may not deny, cancel, or otherwise impose conditions on policies for life insurance, disability insurance, or long-term care insurance based on an individual's status as a living organ donor. The bill also expressly specifies that recovery from organ-donation surgery constitutes a serious health condition that entitles eligible employees to job-protected medical leave. In addition, the Department of Health and Human Services must update educational materials on live organ donation to include information about the benefits of live organ donation and about access to insurance for living organ donors.