As a tennis player he won the Wimbledon Mixed Doubles title in 1912 and 1914. He won the Australian Men's singles and doubles tennis titles in 1912. He was Singles Champion of Europe in 1907 and played for Britain in the Davis Cup. In 1908 he won an Olympic Silver medal in Men's Doubles. He won eight Irish Lawn Tennis Singles titles, four doubles and two mixed titles. Parke was ranked World No. 3 for 1912 by Karoly Mazak, and in both 1913 and 1920 he was ranked World No. 4 by A. Wallis Myers of The Daily Telegraph. He recorded his greatest feats in the Davis Cup where he defeated Norman Brookes and Rodney Heath in the Challenge Round on 28–30 November 1912 when his team, the British Isles captured the Cup and next year he beat Maurice McLoughlin and Richard Norris Williams in the Challenge Round on 25–28 July 1913, though his nation lost the meeting against the USA. He also won the depleted Australasian Championships in 1912.
He played golf for Ireland in 1906 and was also a top-class track and field sprinter and a cricketer. He played chess for the Clones team when he was nine years old. He died in Llandudno, Wales.