For ships operating within range of a starbase, I’ve assumed there are facilities on the base to generate antimatter with which to refuel the starships. This is reinforced by the fact that we can make antimatter today in particle accelerators (though it’s currently the most expensive substance on Earth). Given a few centuries of technological advancement, it stands to reason it could be produced en masse.
For outside-the-norm situations, such as Voyager, where does their antimatter supply come from? Throughout the series, I only recall them ever being concerned with obtaining deuterium (which is, to my knowledge, both one half of the matter/anti-matter reaction material as well as feedstock for the impulse/fusion engines).
The only example I can find of harvesting antimatter is in PRO where they use the Bussard collectors to gather deuterium and use a previously-obtained supply of antimatter. There, we also learn that certain ion storms can produce antimatter.
Memory Alpha mentions the Galaxy-glass Engineering Systems Database contains a technical manual for “Antimatter Generation Replicator Programs”.
So, do 24th century starships simply replicate (or otherwise produce) antimatter using power from the impulse engines that are fueled by deuterium?
One of the things Gene was adamant about was not letting TNG lean on stories about running out of fuel. It had been done so many times in TOS. He wanted the 80-year gap to “solve” that issue.
This is also why the Enterprise-D can regenerate its dilithium. No more “OMG, we don’t have enough dilithium to go to warp!” moments. Which is why you have that moment in Relics when Scotty thinks the crystals are about to fracture and Geordi has to explain to him that they get regenerated inside the chamber.
So it does happen, the Enterprise regularly pulls into a station to get more anti-matter and deuterium, we just never see it because the show is suppose to be about more interesting things.
Like ghost candles.