Molloy started his league career with Shamrock Rovers at 18 but after only a handful of appearances he moved to First Division club Athlone Town in 1996. He immediately hit his stride and ended up the division's top scorer in 1996/97 season earning him a move to St Patrick's Athletic and a shock call up by Brian Kerr to the Ireland squad for the 1997 FIFA World Youth Championships. Molloy played every game and was Ireland's top scorer (3) as they reached the semi final stage only to lose to eventual winners Argentina. Ireland won bronze medals after beating Ghana in the 3rd/4th place play off game.
At St. Pats he linked up with Ireland team mates Colin Hawkins and Thomas Morgan, who had been added to the nucleus of the squad that had won the 1996 league championship, and a lot was expected of the obviously talented squad. All 3 players made an immediate impact with Molloy enjoying a terrific partnership with Scottish striker Ian Gilzean as St. Pats won the league with a dramatic last day win in Kilkenny while arch-rivals Shelbourne lost to already relgated Dundalk. During this season Molloy won the first of his Under 21 caps. The following season was even more of a personal triumph for Molloy as he finished as the league top scorer as St. Pats raced to another league title.
After a disappointing 1999/2000 season Molloy was transferred to Bohemian for a St. Pats record of IR£40,000. Molloy repaid that fee instantly by scoring the winner as Bohemians knocked out Aberdeen FC in the UEFA Cup. However he then got sent off against FC Kaiserslautern in the next round. He would go on to play a vital role as Bohs won the League and FAI Cup double under manager Roddy Collins. The following year was not as successful for Bohs but they did reach the FAI Cup final only to lose to Dundalk FC.
In July 2002, Molloy was again signed by Roddy Collins, this time for Carlisle United of the English Third Division. After only a handful of appearances yielding a solitary goal, Molloy returned to Ireland to play for Shelbourne FC (and become one of a select few players to have played for Dublin football's 'Big 4'. Although Shelbourne finished 2nd in the league that season, it was not a successful season for Molloy and he moved on again, this time to his first club, Shamrock Rovers.
A self confessed Shamrock Rovers fan, commentators saw this as a dream move for Molloy. However he joined a club that had been struggling both on and off the field, as they fought to find a permanent home for themselves. For three years Molloy performed admirably (he was top club goalscorer in 2003 and the Player of the Year in 2004) and his dynamic displays saw him become a hero for the Rovers fans who had a love/hate relationship with him for years. His best efforts, though, were not enough to stop Rovers being relegated to the First division as they lost a two legged play off to Dublin City FC. In total he made 4 appearances in European competition for the Hoops.
With Rovers relegation came financial restraints and Molloy was permitted a move away from Rovers. In January 2006, he re-signed for St. Patrick's Athletic and immediately set about scoring goals, winning April's League of Ireland Goal of the Month.
In January 2007 he joined Motherwell for an undisclosed fee. He left Motherwell by mutual consent in October 2007, having been informed he did not feature in the future plans of manager Mark McGhee.
Trevor signed for Glenavon in December 2007. and was released by the club in June 2011 having not been offered a new contract.