From 1922 until 1934 Jensen was a collector for the Internal Revenue Service. He became president and general manager of the People's Telephone and Telegraph Company.[2]
In 1936, Jensen, a Republican, defeated incumbent Governor Tom Berry as South Dakota Governor. He served from 1937 until 1939. During Jensen's single term as governor, the legislature created a state department to implement the new federal Social Security Act. In addition, despite the financial demands of the relief effort, the Jensen administration was able to balance South Dakota's general fund and eliminate a twenty-year-old overdraft as well as to reduce the state's bonded indebtedness and provide for refunding of rural credit bonds at lower rates of interest. In 1938, the South Dakota Division of the Motor Patrol was formed under Governor Jensen. Harlan J. Bushfield, former Republican state chairman, succeeded Leslie Jensen as governor.[3]
In 1938, Jensen opted to run for a seat in the U.S. Senate, rather than seek reelection to the governorship. However, he was narrowly defeated by businessman Chan Gurney in the Republican primary.
In 1940 Jensen was called to active military duty for World War II, serving in the Pacific Theater as a Colonel commanding the 147th Artillery Regiment, later serving on the staff of the Sixth United States Army. He returned to Hot Springs after the war, remaining active until his death.
