For what it's worth, the incarnation of the Klingon Empire in the Star Fleet Universe (as portrayed in
Prime Directive Klingons) does indeed make extensive use of subject species, albeit ones which have been created for use in the SFU.
The SFU Klingons were themselves a subject (or client) species of a precursor realm, ruled by beings known in modern times as the "Old Kings". Unlike the Hur'q over in Franchise
Trek, the Old Kings did not attack or occupy the Klingon home word directly, but rather negotiated an agreement in which the Klingons (who at the time of First Contact were still in their pre-spaceflight era) would receive a degree of Old King tutelage in exchange for service in the Old King military. A handful of other species also served the Old Kings in this manner, and would in turn be incorporated into the Klingon Empire.
Once the Old Kings abandoned the Alpha Octant and the Klingons reached the point of building a star-faring empire of their own (initially by reaching and re-activating derelict Old King hulls left in their home system), the view they would take of their own soon-to-be subject planets was shaped by this Old King experience. While not quite considered as "politically reliable" as ethnic Klingons, the Empire would allow most of their subject planets to more or less run their own affairs (albeit with a watchful eye from the Klingon secret police to ensure loyalty), would use colonists from said planets to help populate various new colony worlds, and would recruit subject species Marines, technicians, and other enlisted crewmembers for use on Klingon starships. However, the prospects of career advancement for anyone from the subject species would be quite low.
For example, the position of "most trusted subjects" within the Empire proper - not counting the
Vudar Enclave, which is in a distinct category of its own - is held by the Dunkars, orange-skinned humanoids native to a world close to the border with the felinoid
Lyran Star Empire (or hex 1112
on this map). The Dunkar home planet is classed as a major industrial world, and in fact has a slightly higher standard of living than the Klingon capital itself; indeed, the King of Dunkaria is simultaneously Count of the surrounding Klingon province. However, while Dunkars are frequently recruited as colonists and for service in the armed forces, it is quite rare for individual Dunkars to rise up the officer ranks.
While this is by no means on the same level as the degrees of Federation membership provided for in the Star Fleet Universe (and outlined in
Prime Directive Federation), it is a step above the treatment meted out to subject species in certain neighbouring empires - such as in Lyran space, where their counterparts are essentially confined to their respective home planets and placed under harsher conditions.