Halvorsen was one of the sons of Lars Halvorsen, a Norwegian boat builder who immigrated to Australia. After his father's death, the brothers formed a boat-building company Lars Halvorsen Sons. Trygve began to design and build yachts with his brother Magnus, many of the craft proved to be annual Sydney to Hobart race winners. After 1964, he began to build sea-going leisure craft. He retired in 1983.