After returning to England, Orr taught at two schools and at Leeds University. In 1938, he was appointed organist at St. John's College Cambridge. After serving in World War II, he taught at Cambridge and the Royal College of Music.

In 1956, he was named chair of the music department at Glasgow University. Six years later, the founders of Scottish Opera asked him to become its first chairman. He served in the post until 1976, overseeing the company's move into the Theatre Royal. Meanwhile, he was appointed professor of music at Cambridge in 1965, the first Scot ever to serve in the post.

His compositions include the song cycle From the Book of Philip Sparrow, premiered by the Scottish National Orchestra; the operas Hermiston and Full Circle, performed by the Scottish Opera; and the Rhapsody for Strings and Symphony in One Movement.