He started his professional footballing career in his native Northern Ireland with Cliftonville before joining their rivals Linfield in 1954. Having been a key player in the club"s "Seven Trophy" season of 1961/62, he moved to Scotland with Hibernian in 1963 where he made 23 appearances, scoring no goals and moved to Sunderland in 1964. Parke made his debut for Sunderland on 21 November 1964 against Sheffield United in a 3–0 defeat at Bramall Lane.
He went on to make 85 league appearances for the club
He joined Belgian club KV Mechelen before retiring in 1968. He went on to make a further 13 caps for his country, making it a total of 14 caps, with 0 goals.
Parke died of Alzheimer"s disease in 2011, aged 74.