Carter's first jobs as a jazz musician were playing bass with Chico Hamilton in 1959, followed by free-lance work with Jaki Byard, Cannonball Adderley, Randy Weston, Bobby Timmons, and Thelonious Monk. One of his first recorded appearances was on Hamilton alumnus Eric Dolphy's Out There, recorded on August 15, 1960, and featuring George Duvivier on bass, Roy Haynes on drums, and Carter on cello. The album's advanced harmonies and concepts were in step with the third stream movement. In early October 1960, Carter recorded How Time Passes with Don Ellis, and on June 20, 1961, he recorded Where?, his first album as a leader, featuring Dolphy on alto sax, flute, and bass clarinet, Mal Waldron on piano, Charlie Persip on drums, and Duvivier playing bass lines on tracks where Carter played cello.