Bringing Regulatory Advances Into Neuroscience Act of 2021 or the BRAIN Act of 2021 This bill requires the Food and Drug Administration (FDA) to establish the Neuroscience Center of Excellence. The center must develop and implement processes to coordinate FDA activities related to a major disease area or areas affecting the brain or central nervous system. The FDA must also establish and maintain the Neuroscience Translation Working Group to advise the center. If the FDA terminates the center, the working group shall advise the FDA.