Drummond learned jazz from an early age from his father, who was a drummer and a jazz enthusiast and whose record collection included many recordings of Miles Davis, Art Blakey, Max Roach, Buddy Rich and Elvin Jones. He played in bands from age eight and studied at Shenandoah College and Conservatory of Music.
He moved to New York at the behest of Al Foster in 1986 and shortly thereafter joined the Blue Note band, Out of the Blue, with whom he recorded their last album. He joined the Horace Silver sextet, with whom he toured extensively, before joining Sonny Rollins, with whom he toured for three years. He is a long-time member of Carla Bley‘s Lost Chords Quartet, Sheila Jordan‘s Quartet, and the Steve Kuhn Trio. He also leads a New York-based band called Freedom of Ideas. In addition to touring he is Professor of Jazz Drums at the Juilliard School and New York University.
A sideman on over 300 records, Drummond has played and recorded with Nat Adderley, Ralph Moore (1989 and subsequently), Buster Williams(1990–93), Charles Tolliver (1991), Lew Tabackin and Toshiko Akiyoshi, Hank Jones (1991), James Moody (early 1990s), Sonny Rollins, Andy LaVerne (1994), Lee Konitz (1995), Dave Stryker (1996), George Colligan (1997), Ted Rosenthal, Bruce Barth, Andrew Hill (from 1997–2000), Larry Willis (2006 to the present), Toots Thielmans, Freddie Hubbard (mid-1990s), Chris Potter, Eddie Gómez, Stanley Cowell, Javon Jackso.