Sims developed into an innovative tenor saxophone player and played with a number of renowned acts throughout his career, including Benny Goodman, Artie Shaw, Woody Herman, and Buddy Rich. Sims frequently led his own combos and frequently toured with friends Al Cohn and Gerry Mulligan.
House pianist at Scott's club since its opening in 1960, played there and on T.V. with Scott, ZootSims, Al Cohn, Sonny Rollins, Dexter Gordon, Roland Kirk, Ben Webster, Stan Getz, Freddie Hubbard, J J Johnson and many other musicians and singers.
For most of the 60s he was resident pianist at Scott's club, backing numerous visiting jazzmen including ZootSims and Sonny Stitt.
In the middle of the decade he formed a regular band, which included in its personnel at one time or another Bobby Wellins, Peter King and for many years Art Themen.