Complex sentence: After an injury forced him to leave Bob Astor, he stayed a while in New York, playing with Bobby Byrne in late 1942, and then with Charlie Barnet for whom he wrote the classic arrangement of "Skyliner".
Split into simpler sentences: After an injury forced him to leave Bob Astor, he stayed a while in New York. He played with Bobby Byrne in late 1942, then with Charlie Barnet for whom he wrote the classic arrangement of "Skyliner".