Sure. And that's the problem. We can guess at the operational requirements for carriers and fighters, but we are talking about a space game here. Air, sea and land all have their unique way of battling things out. And surface and subsurface warfare is different again.
Accelerate the carrier to warp transition velocity and let the fighters go. They can immediately go to warp and get where they're going. The carrier can stay well clear of the fight. Recovery is ticklish, but the carrier could slow down a bit so that the returning fighters can maintain a larger velocity cushion for maneuvering.
This said, I don't know if the game can handle interaction at those velocities.
We're getting firmly into the realm of gameplay design now. Fighters are just a resource. There is a factory that creates them (and stores them), and the carrier can carry them. Each fighter it launches reduces the number that it carries. Each fighter it recovers increases the number that it carries. Damaged fighters are automatically repaired at some rate on a first-come-first-served basis.
Play with that to your heart's content. Does the carrier pilot have to deploy the carrier in order to allow players to spawn into its fighters? Does the carrier pilot launch fighters or do the players launch their own? Is there some kind of collaboration involved, such as the carrier pilot getting the carrier up to fighter launch velocity, with the fighter pilots choosing their time of launch? Can the carrier design be messed with in terms of numbers of fighters carried, volume of resources available to repair and/or rearm, numbers of simultaneous spawning players, numbers of hangars, numbers of simultaneous service operations, speed of service operations, etc?
Can the factory that creates fighters do the same things as a carrier, except that it's stationary and somewhere safe in friendly space on a planet or moon surface? So if your carriers are all destroyed (or off to war) and you need to defend your fighter factory, do players just spawn up there and defend it directly?
As far as the ship aesthetic is concerned, I described a simple system in a companion thread where a carrier was a long structure with a spine (or spines) that contained fighter bays. That could be taken to the point of having a cruciform cross-section, with essentially a set of 'fighter magazines' side-by-side-by-side, etc. Pop one fighter out and the next one slots into the bay. Rapid fire release the fighters. When a magazine is empty, that bay no longer releases fighters.
Release is to the 'side' of the ship. With the carrier near warp transition speed, the fighter just turns 90 degrees and goes to warp.
Returning fighters are placed at the back of the magazine, to be repaired and rearmed. If there are healthy fighters in front of it, the pilot can transfer to the lead fighter and launch in it. Meanwhile, the magazine services the fighters that it contains in order from first to last.
You could even animate the process of a magazine being loaded into a carrier. Suppose a carrier has space for 20 magazines. Some might not be loaded, giving it a broken spine look. The simplest solution is to always have all magazines in place (fixed geometry). The next simplest is to run the carrier through a structure that puts the magazines in while that part of the ship is hidden (modular geometry).
And then you can play with that forever, with different magazine types and so on. A bomber magazine. A fighter magazine. Magazines with all the characteristics that I assigned to the carrier as a whole. Transferring magazines between carriers. And so on.