Gerald Cleaver was born May 4, 1963, in Detroit, Michigan, the son of drummer John Cleaver Jr. Inspired by his father, he began playing drums at an early age, also playing violin in elementary school and switching to trumpet during junior high and high school. In his teens he gained early experience with Ali Muhammad Jackson, Lamont Hamilton, Earl Van Riper, and Pancho Hagood, later working with Marcus Belgrave, Donald Walden, Rodney Whitaker, A. Spencer Barefield, and Wendell Harrison. He earned a B.A. in music education from the University of Michigan, where a National Endowment for the Arts Jazz Study Fellowship allowed him to study with drummer Victor Lewis, and he joined the university's jazz faculty in 1995.

Now based in Brooklyn, Cleaver is among the most agile and wide-ranging first-call drummers on the contemporary jazz scene, equally comfortable with free playing and swing. He has performed or recorded with Joe Morris, Mat Maneri, whose own career is covered in full in his JazzProfiles.com profile, Roscoe Mitchell, Miroslav Vitous, Yaron Herman, Ralph Alessi, and David Torn. Under the name Veil of Names, he released Adjust on Fresh Sound New Talent in 2001, featuring Mat Maneri, Ben Monder, Andrew Bishop, Craig Taborn, and Reid Anderson, which was nominated for Best Debut Recording by the Jazz Journalists Association. In 2020 he released 27 Licks, an album of drum duos with Devin Gray.

Cleaver's dual fluency in free improvisation and swing, cultivated across decades on both the Detroit and New York jazz scenes and reinforced by his academic grounding at the University of Michigan, made him one of the most versatile and consistently first-called drummers of the contemporary jazz scene.