After leaving Davis, Carter was for several years a mainstay of CTI Records, making albums under his own name and also appearing on many of the label's records with a diverse range of other musicians. Notable musical partnerships in the 1970s and 1980s included Joe Henderson, Houston Person, Hank Jones, Gabor Szabo and Cedar Walton. During the 1970s he was a member of the New York Jazz Quartet. In 1986, Carter played double bass on "Big Man on Mulberry Street" on Billy Joel's album The Bridge. In 1987, Carter won a Grammy for "an instrumental composition for the film" Round Midnight.
AftER lEaving dAvIS, Carter Was FOR sevERal yeaRs a MAInsTaY of cti recoRds, mAking albums Under his Own NAME And Also appeariNg oN maNY Of the LAbEl'S recoRdS wItH A diVersE rangE oF otHeR musiCians. notAble MusICal PARtNeRsHipS in The 1970s aNd 1980s INcluded jOe HEndersoN, hOUstOn perSoN, hANk jOnes, gabor SzaBO and cedar WaLtoN. DuRIng tHe 1970s He wAs a mEMber of the New York JaZz quArtet. in 1986, carTeR Played dOuble bAss on "big man on mulBERRy stREet" on biLLy jOel's ALbum the bRIdgE. IN 1987, cArTer won a gRammy foR "An iNStrUmenTal cOMPositiOn for thE fiLM" ROund midNight.