Billy Clarke joined his home town club Newport County, in 1929 and was signed as professional in November 1930. In 1930-31 he was on the fringe of the first team, but came to the fore the following season in the Southern League – County were voted out of the Football League in 1931 – until moving to Charlton Athletic in April 1932. He failed to make the League side in his short stay at The Valley, though, and returned to Newport in August 1932 following their election back to the Third Division (South). After 46 League games in his two spells at Somerton Park, Billy signed for Portsmouth in July 1934, but made just one appearance, in a 3-2 First Division win at Wolves, before moving along the coast to the Goldstone in May 1935.
Again employed as a reserve, he had just one first-team outing when Len Darling was out with an injury. Billy signed for Aldershot in May 1936, and subsequently played for Crewe Alexandra (signed August 1937). Hereford Town, Accrington Stanley (one month trial in August 1938) and Rhyl before the outbreak of war in 1939. In 1945-46, the last of the wartime emergency seasons, he appeared briefly back at Newport, and subsequently joined Ebbw Vale where he played into his 40s.