Starting with Drumcondra in Dublin, and having been a professional with Everton, Terry Kavanagh played half-a-dozen league games for Exeter in the late 1930s after signing from Notts County. 

Terry played for Drumcondra from 1931 before joining Cheshire County League Wigan Athletic in 1933. Signing for Everton in 1935 he failed to make the first-team and moved to Notts County twelve months later.

After one season and two league outings for the Meadow Lane club, Terry signed for Exeter City in the summer of 1937. Making his debut against the club from where he had just moved in the fourth league games of the season, Terry appeared in five of the following six games without featuring for the first-team again.

Thereafter a regular for the reserves, Terry was released at the end of the season.