Dr. Anthony Fauci is a civil servant at the National Institutes of Health, not a presidential appointee. He would normally continue to serve in the role under a new administration, as has since assuming his post in 1984 as Director of the National Institute of Allergy and Infectious Disease. The infectious disease institute is one of more than two dozen branches of the National Institutes of Health, under the Department of Health and Human Services. Only two Institute leaders are appointed by the president: the Institute's overall director and the head of the National Cancer Center.
Civil servants' positions are generally protected from political pressures, although they can be reassigned to different roles within an organization.