Born on 3 May 1898 to William and Mary Wallace, Martin Kelso Wallace was educated at Methodist College Belfast. Wallace worked as a painting contractor. During World War I, he served in the Royal Naval Reserves.

In 1945, Wallace was elected as a councillor for Windsor ward. He was subsequently elected as an alderman in 1958 and was appointed as High Sheriff the following year. After two terms as Lord Mayor, Wallace was knighted in 1963. He served for nineteen years in the Belfast Corporation, and briefly served on Newtownards council, before retiring in 1967.

During his time as Lord Mayor Wallace welcomed Lord Atlee and the former United States President, General Eisenhower, to Belfast City Hall.

Wallace was chairman of the Belfast Savings Bank in the early 1950s and acted as President of the Belfast Chamber of Commerce. He died on 12 February 1978.