Brennan began his footballing career at Sheffield Wednesday but despite impressing at youth and reserve levels, he never made a first team appearance for the Owls. After being released by Wednesday in the summer of 2000, Brennan came home and went on trial at Bohemians. He made two appearances for the club in the FAI Super Cup but Roddy Collins decided not to sign the midfielder.
Brennan then went on trial at Luton Town and this time it was more successful, earning a two-year contract at Kenilworth Road. He made his debut for the club in a 2–1 defeat at Wigan Athletic soon after. However, he never became a regular at the club and in 2002 moved to Hitchin Town.
Luton would prove to be his last taste of League football as he drifted around the non-League scene with spells at Stevenage, Grays Athletic, Lewes, AFC Wimbledon, Cambridge City, Chesham United and Hemel Hempstead Town in the following years. In his brief spell with Wimbledon he earned the nickname "the Irish Beckham", a reference to his crossing ability. While at Grays he helped them win the 2004–05 FA Trophy.
In August 2009, Brennan signed for Spartan South Midlands Football League Premier Division side Aylesbury. In 2010, he rejoined Hemel Hempstead Town, and in March after the sacking of manager Gary Phillips, he was appointed as caretaker manager at the age of just 29.
Brennan began a second spell with Dunstable Town at the start of the 2011–12 season. He joined as player/coach and managed the team in cup ties. In May 2012 he rejoined Hemel Hempstead Town this time as manager. He helped the Tudors to their highest ever finish (fourth in Southern League Premier Division) this meant that they had qualified for the playoffs. They reached the final against Gosport Borough, where they drew 2–2 which sent the game to penalties which was lost 5–4.
The following Season saw promotion to the Conference South, after winning the Southern Premier League by 10 clear points.
After a disastrous start to their first season in the Conference South league, Hemel finished in a creditable 9th position. Also they reached the First Round of the FA Cup, losing at Bury 3–1, this after taking the lead by James Potton. As Bury scored two late goals to take them through.
The 2015–16 National League South season saw Brennan's Hemel just miss out on the playoffs as Whitehawk pipped them on the last day, to that all important fifth place.