Ballybough, Dublin born centre forward Paddy Moore began his football career with Cloncliffe Celtic and played for Dublin junior club Bendigo from 1926 before a brief spell at Richmond Rovers in 1928. From there he joined League of Ireland club Shamrock Rovers in 1928 and in the summer of 1929 he was signed by Second Division Cardiff City, making his Football League debut, and only appearance for The Bluebirds, in a 4-1 defeat at Charlton Athletic at the end of August.
In March 1930 he joined Merthyr Town and played 5 matches for them between March and early April as they struggled against re-election, a struggle they ultimately lost. In June 1930 joined Tranmere Rovers where he had a further brief spell in English football making 4 appearances in the late summer before returning to Shamrock Rovers, and he had considerable success at the club, winning The FAI Irish Cup in 1931, and the League of Ireland Championship and League of Ireland Shield in 1932. While with Shamrock he won the first of his 9 caps for The Irish Free State when he played and scored in a 1-1 draw against Spain. In all he scored 7 goals during his Irish Free State matches, including all 4 in a 4-4 draw with Belgium in February 1934, winning his last cap against Hungary in December 1936.
In May 1932, Scottish League club Aberdeen paid £1,000 for Moore’s signature to replace Benny Yorston, and he made his Scottish League debut in a defeat at Celtic that August. His debut season was prolific, Moore netting 28 goals in their 1932-33 campaign, and he followed this up with a further 18 goals in 1933-34. It was while at Aberdeen that he played for Ireland, winning a single cap in a 1-0 defeat to England at Bloomfield Road, Blackpool in October 1932. However the emergence of the partnership between Matt Armstrong and Willie Mills sidelined Moore during his third season, and after 47 goals in 74 appearances for The Dons, he returned to Shamrock Rovers in July 1935.
More success followed, Moore winning The FAI Irish Cup in 1936, before he joined Shelbourne in 1937, playing the 1937-38 season with The Shels before a move to Brideville in 1938. He then returned to play for Shamrock Rovers before his eventual retirement.