Ged began his career with Tranmere making 238 appearances and scoring 20 goals in the period 1990-1996. A move to Maine Road in 1996/97 brought another 43 games and 4 more goals until he fell out of favour with manager Joe Royle.

Following injuries to Shaun Carey, Neil Adams and Mike Milligan early in the 1998/99 season, manager Bruce Rioch entered the transfer market to bring Manchester City's dissatisfied midfielder Ged Brannon to Carrow Road. He made his first appearance in a Yellow shirt in the Reserve team clash at Charlton on 19th August 1998. A total of 12 games were played for the Norwich first team.

After two months at Carrow Road, Bruce Rioch decided not to sign Ged on a permanent contract as Adams and Milligan had returned to fitness. Thanking Ged for his contribution to the Norwich cause, Rioch revealed that Ged was not the style or type of player that he thought the Norwich midfield needed now that injury worries had diminished. On his return to Maine Road on 26th October 1998, Ged immediately parted company with Manchester City and signed for Scottish side Motherwell for £376,000.

Ged received an international call up to play for the Cayman Isles on the 29th February 2000. Other league players called up include Fulham duo Barry Hayles and Wayne Collins, Birmingham's Martin O'Connor and Chesterfield's Jason Lee although not all of them accepted. However intervention by FIFA put an end to this scheme by the Cayman Isles.

In December 2000, it was reported that Ged and fellow Motherwell player John Spencer were expected to head for the USA at the end of the season and join the Miami Fusion on a Bosman transfer. However this move may be scuppered by the opportunity to return to North West England with either Tranmere or Wigan who have both been linked via Teamtalk. Motherwell's financial situation meant that they could not risk losing out on a potential fee for Brannon. Thus on February 16th 2001, Ged signed for Bruce Rioch's Wigan for £175,000.

Out of favour at Wigan at the beginning of 2003, Ged returned to Scotland signing on loan for Dunfermline. He returned to Wigan at the end of the season but was sidelined, playing only for the Reserves. In mid-September 2003, he joined Rochdale on a month's loan. He replaces midfielder Robert Betts with whom Dale could not agree a new contract. Although Alan Buckley (the Rochdale manager) rates Brannan highly and would like to extend the loan, the move is unlikely to become permanent as Rochdale could not afford him. Ceefax reported on 9th October that Ged was likely to extend his stay at Spotland. This lasted for a second month with Ged returning in early November. On 25th November 2003, Ged signed a two year deal with Accrington Stanley.

At the end of September 2005 and no longer part of Stanley's first team plans, Ged and Accrington parted company by mutual consent. By early October, he had signed for Radcliffe Borough. A month later and Ged was back in the Conference, having signed for Morecambe. Following Morecambe F.C's promotion to the football league after a 2-1 victory over Exeter City, Brannan announced his retirement from the game after leading the team up to collect their winners medals and play-off trophy.

Ged Brannan came out of retirement in November 2007 to sign for Vauxhall Motors of the Blue Square Conference North. In October 2008, he moved to their Conference North rivals Burscough to be player-coach.

By 2022 he was the Under-23s manager at Accrington Stanley. He returned to Morecambe to coach their youth team and then on 27th November 2023 was appointed as manager on an 18 month contract replacing Derek Adams who had quit to join Ross County.

He left Morecambe on 30th April 2024 to become Assistant Manager at Accrington with his friend John Doolan in the manager's position. He signed a three year contract after the clubs agreed compensation.