Parry played for Derby Boys and signed for the Rams in July 1948, a time when Raich Carter and Billy Steel were at the club.
A one-club man, Parry remained at The Baseball Ground for 20 years and set a club record 482 League appearances up to the 1965–66 season (517 in total) until Kevin Hector overtook it.
Parry's best scoring season was 24 goals in 34 League games in 1955–56 but was injured by Ray De Gruchy's challenge playing Grimsby Town at The Baseball Ground in March 1956.
The back injury sustained in the game meant Parry was sidelined for the rest of the season and without his goals, Grimsby went on to win the Third Division North and take the only promotion place.
In the Second Division Parry became club captain and converted to wing-half but eventually lost his place in the 1965–66 season before moving on to Boston United.