The 2014/15 under19 season saw Brennan play with Bray Wanderers. At the end of that season, he left the Carlisle Grounds and joined UCD U19s for the short transition season. Ahead of the 2016 season, he had joined Cabinteely FC where he made 26 First Team appearances during the season.
Bohemian's manager, Keith Long, came calling before the 2017 season and Oscar joined the Dalymount club, making 29 league appearances that season. Having re-signed for the 2018 season, he made a further 25 league appearances for them.
Oscar Brennan signed for Shelbourne, then under the management of his former team-mate at Dalymount, on November 14th, 2018.