Chronic Kidney Disease Improvement in Research and Treatment Act of 2021 This bill modifies provisions relating to Medicare coverage of treatments for chronic kidney disease. Specifically, the bill expands the Medicare annual wellness visit to include chronic kidney disease screening and allows certain Medicare beneficiaries who have End Stage Renal Disease (ESRD) to enroll in Medicare supplemental policies. It also (1) provides for alternative payment methodologies for certain new drugs, biologics, and devices that are renal dialysis services; (2) revises quality measures; (3) establishes an incentive payment methodology; and (4) increases access to kidney disease education services. The bill also extends the coordination period (from 30 months to 42 months) during which private health insurers may serve as the primary payers for Medicare beneficiaries with ESRD.