Sjur Lindebrække became Doctor of Law in 1948. He was Assistant Manager of Bergen Privatbank in 1940-1945 and Bank Manager in 1945. He was Managing Director later in 1958-1968 and was active chairman of the Board in 1968-1976. He was Chairman of the Norwegian Banking Association in 1954-1960.
Lindebrække was a member of the Storting in 1945-1953. He sat on the board of the Conservative Party in 1950-1982 and was chairman of the party in 1962-1970. He tried to bridge the dividing lines between the non-socialist parties and was highly respected also by enemies of his party. Sjur Lindebrække was a member of the Norwegian Nobel Committee in 1976-1981.