Carter began his career as an assistant lecturer in geology at the University of Otago in 1963 and advanced to senior lecturer after obtaining his Ph.D. in 1968. He was professor and head of the School of Earth Sciences at James Cook University from 1981 to 1998, an adjunct research professor at the Marine Geophysical Laboratory at James Cook University from 1998 to 2005 and a visiting research professor in geology and geophysics at the University of Adelaide from 2001 to 2005.