He was a winger. Brennan began his career in his home country of Northern Ireland, firstly with Harland and Wolf Welders and then Bloomfield United and Distillery. He moved to England in 1947 to join Luton Town. He subsequently moved to Birmingham City in 1949 and Fulham in 1950.
Brennan"s first spell with Norwich lasted from 1953 to 1956.
He left the club to play for Yarmouth Town before returning to Norwich in 1957. In the semi-final against his former club Luton, Brennan scored Norwich"s equaliser in the first match at White Hart Lane before the team lost the replay at Street Andrews, Birmingham.
Brennan left Norwich for the second time in 1961 to join King"s Lynn F.C. as a coach.