Born on a ranch near Big Timber, Montana, Fjare attended public schools. He was employed as a clerk in a clothing store at Big Timber, Montana, and later became part owner. Enlisted as a private in the United States Army in 1940. Commissioned a second lieutenant of Artillery in 1942. He served as a pilot in the South Pacific and was discharged as a captain in 1946. He served as member of the Montana Public Welfare Commission 1952-1954. He served as member of board of trustees of Big Timber Public Schools 1951-1954.
Fjare was elected as a Republican to the Eighty-fourth Congress (January 3, 1955-January 3, 1957). He was an unsuccessful candidate for reelection in 1956 to the Eighty-fifth Congress. He served as member of State house of representatives in 1959. He engaged in the life insurance business. He was an unsuccessful candidate for election to the United States Senate in 1960. Advertising director, Montana State Highway Department from 1962 to 1969. He served as director of Montana Federal Housing Administration 1970-1979. He is a resident of Big Timber, Montana.