Ulster were the first Irish side to win Europe's premier club competition when they beat Colomiers at Lansdowne Road back in 1999.
But that success, achieved during a year when English clubs boycotted the tournament, has since been overshadowed by the triumphs of provincial rivals Munster and Leinster, who have won two titles apiece.
The pair have been perennial European challengers over the course of the last decade, a time during which Ulster occasionally struggled to keep up.
But under the guidance of coach Brian McLaughlin, and with a squad mixing the experienced South Africa contingent of Ruan Pienaar, Pedrie Wannenburg and Johann Muller with homegrown talents like Trimble and Craig Gilroy, Ulster are back at the European game's top table.
Victory would stop 2011 winners Leinster becoming the first side to retain the trophy, and give Ulster coach Brian McLaughlin European club rugby's biggest prize in his final game in charge.
But Ireland wing Trimble says the chance to prove that Ulster are no longer the "third-choice province" is a hugely potent form of motivation for the Twickenham showdown.
"This game mean a massive amount for Ulster rugby and for Irish rugby, there is such a rivalry between the provinces," he said.
"We have become genuine contenders for the trophy and Saturday is an opportunity we don't want to let slip.
"Playing Leinster adds intensity and passion and we want to come out on top and we also want to deny Leinster that trophy."
He added: "We were getting fed up of being seen as the third-choice province.
"I have played for Ulster for seven or eight years and we have always been seen as third-choice behind Leinster and Munster.
"Going into this final we are motivated by jealousy. We want to leapfrog them and become the number one province.
"We have done a lot of hard work to get to this point and a Heineken Cup final gives us a great chance to do it.''
Trimble, then 14 years of age, was among the crowd in Dublin when Ulster last won the trophy, with full-back Simon Mason booting six penalties in their 21-6 win.
And the 27-year-old hopes to see similar scenes of celebration come Saturday evening.
He said: "I was there in '99. I don't remember all that much about it although I don't think we played much rugby, but it was one of those days when we squeezed out a result.
"I just remember that Lansdowne Road was white and it was a very special day.
"We have finally been given an opportunity back at that level but we don't want to let it pass us by because you don't know when your next Heineken Cup final will be."
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