The conquered planets serve the Empire. If they rebell then action would be taken against them.
Yet the thing is, there are no examples of this really happening. Klingon designs on Organia were thwarted. Krios was never indicated to be anything but a Klingon colony. No members of species other than the "one and only" Klingons ever served aboard Klingon ships or installations (evident now that the forehead thing was finally sorted out). Etc.
The Son'a had subjugated races in their servitude. The Grand Nagus had alien servants. Kirk had an alien lackey, Picard had dozens at least. The Klingons? They only ever served each other! And aliens within the Empire only served prison sentences...
Why would they have their subject races serving on their ships, particularly their warships? Better to keep the trapped on their planets where they can't cause trouble. Even if they served on a freighter would the Klingons trust a subject race with a projectile that could be crashed into a planet at near lightspeed and is loaded with antimatter? Even an unarmed starship is extraordinarily dangerous. Better to have lower ranked Klingons do the hauling and leave the conquered races to do the hewing and farming and mining.
Why did we never see them? Because they live a boring existence.