Born and raised in Harlem by a pianist mother and a stepfather who played trumpet, he was introduced to jazz by his uncle Kenneth Bright, a major shareholder in Circle Records and the manager of rehearsal spaces above the Lafayette Theater.
Sims studied percussion at the High School of Music and Art and at the City College of New York, where he played tympani in the CCNY Orchestra.
When he returned to jazz in the late 1970s, he usually inserted "La Roca" into his name in quotation marks to help audiences familiar with his early work identify him.
Between the end of the 1950s and 1968, he also played with Slide Hampton, the John Coltrane Quartet, Marian McPartland, Art Farmer, Freddie Hubbard, Mose Allison, and Charles Lloyd, among others.
[6] With Anamari With Bill Barron With Paul Bley With Rocky Boyd With Jaki Byard With Sonny Clark With Johnny Coles With Ted Curson With Art Farmer With Don Friedman With Slide Hampton With Joe Henderson With Freddie Hubbard With Steve Kuhn With Scott LaFaro With Booker Little With Charles Lloyd With Jackie McLean With Helen Merrill and Dick Katz With J.R. Monterose With Sonny Rollins With George Russell With Tony Scott With Paul Serrano