I figured I'd try outsourcing some of the research on this one. I have a list of a handful of characters like this from Trek but I figured I'd take feedback on this.
It's handy for Foundry authors because we can use these characters in The Foundry. It might also be handy for Cryptic.
Off the top of my head, there were a number from Voyager, including Kim's neighbor, Ensign Baytart, who was mentioned several times but never shown. DS9 had Felix, creator of the Vic Fontaine holoprogram and a number of Dominion War casualties, who may be useful in time travel missions or have surviving family members. TNG had Geordi and Leah Brahm's three kids, Sidney, Bret, and Alandra, who have been mentioned as existing in STO's timeline.
This kind of thing is really handy because it allows authors (or Cryptic) to feature a character who was present for a Trek event that feels somewhat authentic without having weird likeness dodges or people who "heard it through the grapevine."
So, for example, if a threat from the Delta Quadrant shows up, we can get briefed by, say, Admiral Baytart who can cite his experience on Voyager.
You can create a new Voyager crewman, sure, but I think it adds something to have a character mentioned (but never seen) show up.
I'd like to produce a master list but it'd be handy if any names or implied characters jump out at people.
He nearly replaced Tom Paris and was basically Voyager's second best pilot, always mentioned as a backup to Paris. He was also a skilled juggler who appeared on a show Neelix hosted and hated Kim's clarinet practice.
One of my most (if not the most) favorite foundry missions features Barclay's daughter. There was also Lieutenant Ayala who might be a bit fudgy due to appearing in 120 episodes of Voyager, but is still more likely because he was never more than an extra. Same goes for Lieutenant Kyle.
Didn't Kirk have a brother that never actually showed up on screen?
Yes, though an extra played his brother's dead body on a floor in the episode with what my cousin calls the "Flying Fried Egg Monsters". (Operation: Annihilate"? I can't recall the name just now). So technically his brother did appear on screen.