Clarence Leslie Baldwin Estey was born on June 29, 1917, in Saskatoon, Saskatchewan, to James Wilfred and Muriel Alice Estey. He received his early education in Saskatoon at Albert School, Victoria School and Nutana Collegiate. Estey earned a Bachelor of Arts degree in 1938 and a Bachelor of Laws degree in 1940 from the University of Saskatchewan. He was called to the Bar of Saskatchewan in 1941. Estey enlisted in the Canadian Army in 1941 and was wounded in action in France in 1944. He returned to Canada and was discharged.
Prior to his entry into politics, Estey practised law with the firm of Moxon and Schmidt in Saskatoon. He was appointed Queen's Counsel in 1956. Estey sat on the Saskatoon Public School Board for several terms during the 1950s and 1960s and also served as its chair.
Estey was elected to the Saskatchewan Legislature in 1967 and served as the Liberal Party Member of the Legislative Assembly for the Saskatoon Nutana Centre constituency until 1971. He served in the Ross Thatcher Government as Minister of Municipal Affairs (1967-1970); Minister of the Saskatchewan Indian and Métis Department (1969-1970); Minister of Industry and Commerce (1970-1971); and Minister Responsible for Saskatchewan Power Corporation (1970-1971).
Following his defeat in the 1971 election, Estey returned to his law practice. He was appointed as a justice of the Court of Queen's Bench in 1974 and served on the bench until his retirement in 1992. Clarence Estey died in Saskatoon on March 5, 1995.
Clarence Estey married Virginia Grace Smith on August 17, 1945. They had three children: Jean, Susan and James.