Half-back Tommy Barrett was born in Scotland and started his career with Hibernian in Edinburgh. In October 1953 he was transferred to Hamilton Academicals who were at the time playing in the Scottish First Division. Tommy played in 61 league games for Hamilton Accies and scored four goals.
In 1959 Tommy moved to Montreal and joined Canadian Alouettes in the National Soccer League. The Alouettes won the 1959 Canadian Challenge Trophy. Tommy played at left half in the 3-2 win over Westminster Royals in the Trophy final.
The Canadian Alouettes changed their name to Concordia before the start of the 1960 NSL season. Tommy was captain of the team of the team as they finished in third place in the league standings.
In the 1961 season Concordia joined the International Soccer League that was operated by Bill Cox. Concordia played in a group consisting of Bangu (Brazil), Besiktas (Turkey), Dinamo Bucharest (Romania), Everton (England), Karlsruhe (Germany), Kilmarnock (Scotland) and New York Americans (U.S.A.). Concordia finished in sixth place in their group.
The club also played in the National Soccer League and also entered a team in the Canadian Challenge Cup. Concordia finished in second place in the NSL standings and also won the Canadian Challenge Trophy. Tommy was Concordia’s captain during the 1961 season. The club stopped operating after the 1961 season.
Tommy joined Montreal Hungaria before the 1962 season. The club finished in third place in the Quebec National Soccer League championship. Tommy played with the Cantalia team in the 1963 season. The club played in the Eastern Canada Professional Soccer League.
In 1964 Tommy played for Montreal Italia in the Eastern Canada Professional Soccer League. After the season Tommy was picked as the left half on the ECPSL second all-Star team.
Tommy joined Montreal Italica before the start of the 1965 season. Italica won the 1965 Eastern Canada Professional Soccer League. In a vote after the season he was picked as the fifth best player in Montreal soccer.