Complex sentence: In the 1940s he worked on film scores in Hollywood, but he was blacklisted during the McCarthy era; unable to work in Hollywood, he moved back to New York, where he headed the music program at Elisabeth Irwin High School.
Split into simpler sentences: In the 1940s he worked on film scores in Hollywood, but he was blacklisted during the McCarthy era. Unable to work in Hollywood, he moved back to New York, where he headed the music program at Elisabeth Irwin High School.