Born in Camelon, Falkirk, as a schoolboy Corbett captained the Falkirk team that won the Scottish Schools Trophy. He also played for Scotland Boys and, while at Musselburgh, played for Scotland Juniors. He signed for Hearts at the age of 15.
Norman Corbett played for West Ham United between April 1937 and 1950, making 166 League appearances and scoring three goals for the club. He was an ever-present for the Irons during the 1947-48 season, and won a Football League War Cup winners medal in 1940, although he did not appear in the final.