Vieques Recovery and Redevelopment Act of 2021 This bill provides a framework to compensate certain residents of the island of Vieques, Puerto Rico, for the use of such island for military readiness. The bill sets forth provisions regarding award amounts for individuals and for claims by the municipality of Vieques. An individual claimant who has resided on the island of Vieques for not less than five years shall be awarded monetary compensation if the claimant contracted a chronic or life threatening case of cancer, hypertension, cirrhosis, kidney disease, diabetes, or heavy metal poisoning during or after the government used the island for military readiness. The bill limits total amounts awarded to $1 billion and bars claims not filed within 15 years of enactment.