His first professional job was as a staff arranger for Design for Listening, an NBC radio show based in his hometown.
In the latter part of the decade he began working on Broadway, orchestrating for Shinbone Alley, The Music Man, Fiorello!, and West Side Story.
His work on the latter resulted in his being hired to score the 1961 screen adaptation with Saul Chaplin, Johnny Green, and Sid Ramin.
For the remainder of his life, Kostal divided his time primarily between stage and screen, with an occasional detour into television to work with such people as Carol Burnett, Lucille Ball, and Leonard Bernstein.
At the time of his death he was a widower (his wife Sylvia had died the year before), and president of the American Society of Music Arrangers and Composers.