Advanced Recycling Research and Development Act of 2021 This bill requires the Department of Energy to implement research, development, and demonstration programs to (1) accelerate innovation in energy-efficient recyclable plastics, next-generation plastics, and composites recycling and upcycling strategies and technologies; and (2) support the development of advanced materials for batteries and innovative technologies to reclaim and recycle critical materials from advanced and lithium-based battery technologies used in consumer electronics, defense, stationary storage, and transportation applications.