Veterans Infertility Treatment Act of 2021 This bill requires the Department of Veterans Affairs (VA) to furnish infertility treatments, standard fertility preservation services, or both to a covered veteran or partner of a covered veteran if the individuals jointly apply for such treatments or services. A covered veteran is a veteran who has infertility and is enrolled in the VA health care system. Under the bill, in vitro fertilization treatment may only be furnished for up to three completed cycles resulting in live birth or six attempted cycles, whichever occurs first. The VA may furnish in vitro fertilization treatment using donated gametes or embryos. During the interim period before infertility treatment regulations are in effect, the VA must ensure that (1) fertility counseling and treatment for veterans may also be furnished to the partner of a veteran regardless of whether the veteran and the partner are married, and (2) such counseling and treatment may be furnished using donated gametes or embryos.