Jarman served as assistant State examiner of accounts in 1919–1930, and as Secretary of State of Alabama in 1931–1934. He served as assistant State comptroller in 1935 and 1936. He was a member of the State Democratic executive committee of Alabama in 1927–1930.
Jarman was elected as a Democrat to the Seventy-fifth and to the five succeeding Congresses (January 3, 1937 – January 3, 1949). He served as chairman of the Committee on Memorials (Seventy-fifth Congress). He was an unsuccessful candidate for renomination in 1948.
A big, good-natured Rotarian type of man who has always supported the Administration's foreign policies to the full. Is reputedly pro-British and is likely to back any international post-war attempts by the Administration, although he is no out-and-out New Dealer.
He was appointed by President Harry S. Truman as Ambassador to Australia on June 8, 1949, and served until July 31, 1953. He died in Washington, D.C., on February 17, 1955, and was interred in Arlington National Cemetery.