Neuroscience Center of Excellence Act of 2021 This bill requires the Food and Drug Administration (FDA) to establish the Neuroscience Center of Excellence to address neuroscience diseases and disorders (e.g., addiction, Alzheimer's disease, and psychotic disorders). The center must carry out various activities, including (1) coordinating with FDA programs that focus on certain areas, such as drug evaluation; (2) convening periodic public meetings to engage with stakeholders to address challenges associated with developing medical products for neuroscience diseases and disorders; (3) establishing a program to facilitate the collection and systemic use of patient experience data to develop such medical products; and (4) convening a public meeting to discuss how to promote equity and the inclusion of traditionally underrepresented populations in the development of such medical products. The FDA must take actions related to these issues, such as issuing final guidance with recommendations on the collection and use of patient experience data for developing such medical products. The Government Accountability Office must report to Congress a study that (1) reviews the participation of traditionally underrepresented populations in clinical trials for such medical products, and (2) provides recommendations for improving the participation of these populations.