As a youth Moore played for several teams including Richmond Rovers before joining Shamrock Rovers for the first of three spells. In 1929 at the age of 19 he signed for Cardiff City, but made only one appearance. After brief spells with both Merthyr Town and Tranmere Rovers he then returned to Shamrock Rovers. During the 1931–32 season he helped Rovers win both the League of Ireland championship and the League of Ireland Shield. He also helped Rovers win the FAI Cup in both 1931 and 1932, scoring in both finals.