There might be a fairly ordinary reaction as with a rocket, but it’s invisible and has no effect, so it can be disregarded. We know about dark matter, so why not a dark matter rocket?
However, the usual reason for having a “space drive” is to save on the energy needed to come up to speed, and allow accelerations that would crush the crew if done in a normal way. So we probably don’t want rockets at all.
If you have some novel way of getting up to speed etc. but handwave away the momentum issue by saying it’s carried away by dark matter emission, you still have the normal rocket equation applied to the energy needed to carry away the balancing mass.
Slower Than Light but still Warp Drive
Perhaps the ship doesn’t move through space at all, but a bubble of space containing the ship can move. Normally we want a ship that’s not in hyperspace or jumping or whatnot to be present in space so it can experience the universe around it (e.g. run into things). So having a warp/hyperspace/jump mechanism and then making it slower than light (due to causality rules?) is a bit odd.
Shared with Warp Technology
But we can get some mileage out of having a common mechanism between the Warp Drive (hyperspace, jumps, whatever) and the “sublight” engines. The ship moves through space in the normal way. But the engines use the FTL technology to transfer energy and momentum through wormholes, warp space, or whatever. This has the advantage of using common mechanisms, always good to do.
Think of an analogy of the Cable Cars, as San Francisco is famous for. It reaches below the street to grab a cable, getting its drive power that way from an engine located elsewhere in the city. The engine does not have to move itself or its fuel. The delivery of energy/momentum is invisible to normal cars on the road.
The engine on the space ship could reach into another dimension, through a wormhole, hyperspace, or whatever. The ship itself doesn’t travel through the subspace, but the energy and momentum does. The analogy provides what we specifically want for the space ship: it does not need to carry its own power source and fuel, freeing us from the tyranny of the rocket equation.
It can use a central power source, or it could use a system of energy and momentum buffers to save consumed power. Consider that a ship going one way and another ship going the opposite way will, as a pair, balance momentum. And ships do tend to go back and forth along the same route. The subspace cable system could connect to a buffer of some kind that allows momentum to be moved between opposite uses rather than simply lost. Likewise for energy: if you can recover the breaking energy, you will save a huge quantity of energy.
Imagine the subspace engines can connect to each other, dialed up at a desired address. Two ships can push against each other, through their engines via subspace. Or, a ship can get pushed by a huge reaction wheel, and likewise can break against the opposite side of the same wheel.
You can further note that using the hyperspace technology for this approach can always avoid causality violation rules that FTL travel would run into.
In general, if a conserved quantity appears to be violated, you just found another form of that quantity. Energy can be consumed in so many ways it is easy to lose track of. Angular momentum can go into magnetic fields (and invented new fields) as well as spinning objects. But linear momentum really has to be mass or massless particles moving, taking a certain amount of energy to do that. This brings us back to the invisible rocket.
So, lose the momentum in a different universe. But, as with the invisible rocket, you want to get energy and momentum, not spend it. So suppose this universe has momentum streams you can tap into, like rivers or the street cables. This is like the hyperspace tech sublight engines, but with a natural source. If you think of it like wind or water currents, you might “sail” them by probing to the desired depth, and this could give you limits as to what’s available: complete with storms and doldrums. That gives rich plot fodder right there.
Since the streams are everywhere, it is not some sneaky FTL, so you don’t have to worry about causality violation at all. And the same mechanism gives you unlimited energy more generally for your society.
Maybe your drive “pushes” against all the mass in the universe. It appears to be a reactionless drive, but the balance is spread over everything. This has its own problems regarding FTL causality. It’s a quick handwave for whatever X design you already have and need to lampshade the conservation law.
In terms of using it as a principle to design a space drive, you still have the issue of bringing all the energy and generating a difference in momentum, so you might as well use a more ordinary invisible rocket.