Paddy Brennan was born in 1924 in Dublin. He came to prominence with League of Ireland club Shelbourne before signing for Brighton & Hove Albion in 1948. He made his Football League Third Division South debut towards the end of the year, and became a regular in 1949–50, but inconsistency cost him his place, and he made just six senior appearances in two years.
He spent a season with Yeovil Town before joining Southern League rivals Weymouth where he made 112 appearances in all competitions. A season with Dover preceded a return to the Brighton area where he was player-coach of Sussex County League side Hove Town and worked as an ambulance officer.