Leavey was selected to play in Liverpool's forward-line on just five occasions, all during the 1910/11 first division campaign. He replaced regular centre-forward Jack Parkinson for two games at the end of 1910; the Christmas Eve and Boxing Day fixtures against Aston Villa and Sunderland respectively and then made three further appearances in April 1911 just before the season finished. Leavey's most productive spell came at Plymouth Argyle in the Southern league where he played 80 games from 1907-1910 apart from a four-month spell at second division Derby County where he made no appearances before returning to Plymouth. He was on Barnsley’s books who won the FA Cup in 1912 but missed out on the final as he broke his leg in the third replay of the quarter-final victory over Bradford City.