Collaborative Academic Research Efforts for Tourette Syndrome Act of 2021 or the CARE for Tourette Syndrome Act of 2021 This bill requires the National Institutes of Health (NIH) to carry out data collection and expand other research activities on Tourette syndrome. This is a neurological disorder characterized by sudden, repetitive, rapid, and unwanted movements or vocal sounds. Specifically, the NIH must develop a system to collect epidemiological data and information on the availability of medical and social services for individuals with Tourette syndrome and their families. In addition, the NIH must award various grants for research on Tourette syndrome, including to support Collaborative Research Centers for Tourette Syndrome. The NIH must also designate a portion of its funding for Tourette syndrome programs and activities.