Richard Hageman appeared in THE GEAT CARUSO (1951). Herbert Stothart and Bronislau Kaper were seen in an MGM short as well as Boris Morros and Victor Young in a short about the scoring of WELLS FARGO (1937).
Danny Elfman - singing in Back to School James Horner - running around Enterprise in ST2
Elfman has appeared numerous times with Oingo Boingo in films. There's also more acting-related and/or cameo parts in I NEVER PROMISED YOU A ROSE GARDEN (1977), FORBIDDEN ZONE (1980) or Sam Raimi's THE GIFT (2000?), just to mention three. They have all been mostly because he had a connection to the director of some sort.
All the ones I know are already up, so the closest I can give you is arranger/conductor Jonathan Tunick conducting the pit orchestra in A LITTLE NIGHT MUSIC.
Elmer Bernstein appears very briefly in the " The Man with the Golden Arm " and, of course, has a small but significant role in " From Noon Till Three "