Moncur was born in New York into a musical family, as the son of jazz bassist Grachan Moncur II and nephew of saxophonist Al Cooper. After high school he toured with Sonny Rollins and Ray Charles among others, as well as featuring on two of Jackie McLean’s albums. Moncur’s albums as leader for Blue Note demonstrate his otherworldly ear for composition and arrangement, and gracefully fuse hard bop and free jazz. Later Moncur joined Archie Shepp’s ensemble, and recorded with Cassandra Wilson, while also teaching at Newark Community School of the Arts.