Preventing Lead Poisoning Act of 2021 This bill requires coverage under the Children's Health Insurance Program (CHIP) of screening blood lead tests. Specifically, CHIP must cover a child's test once at the age of 12 months and once at the age of 24 months, or once between the ages of 24 months and 72 months if the child has never been assessed, as well as testing at such other times as recommended by a child's health care provider. The bill also provides statutory authority for these requirements (regarding testing intervals) for state Medicaid programs.