Trappier played with Charlie Skeets and Blanche Calloway in the late 1920s. After working steadily through the 1930s, he joined Fats Waller in 1941-42 before serving in the military during World War II. He led his own trio in various hotels in New York City in the 1950s, and played as a sideman into the 1970s. Among those he played with are Josh White, Wilbur De Paris, Edmond Hall, Sy Oliver, Hot Lips Page, Buddy Johnson, Wingy Manone, Sidney Bechet, Benny Goodman, and Red Allen.
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- With Rex Stewart
- Rendezvous with Rex (Felsted, 1958)