Brustad studied at the Oslo Conservatory and at several schools throughout Europe. He was a solo violist with The Oslo PSO from 1929-43 and took a teaching position at the Oslo Conservatory in 1937. In 1953 he received a state pension for life. Brustad's early compositions differed greatly from the Griegian style, earning him a position at the forefront of radical Norwegian music. His compositional styles range from the influence of French impressionism to neo-classicism, nationalism and expressionism.