Soon after, he played with guitarist Alvino Rey in New York City, then toured with the Glenn Miller band in the early 1940s.
[citation needed] During the rest of the decade, he worked with Louis Armstrong, Roy Eldridge, Ella Fitzgerald, Bud Freeman, Woody Herman, Jerry Jerome, Bernie Leighton, Ray McKinley, Frank Sinatra, and Muggsy Spanier.
In the 1950s and early 1960s, he recorded as a sideman with Don Elliott, Coleman Hawkins, Gene Krupa, Mundell Lowe, Buddy Rich, Artie Shaw, and the Sauter-Finegan Orchestra.
Alpert's only album as a leader was Trigger Happy (Riverside, 1956), which he recorded with Al Cohn, Urbie Green, Tony Scott, Ed Shaughnessy, Zoot Sims, and Joe Wilder.
[1] He was a member of the CBS Orchestra with a rhythm section of Hank Jones, Sonny Igoe, and Chuck Wayne until the late 1960s.