Priam was a star system in the Alpha or the Beta Quadrant.

Its system had a number of planets, including Priam IV, a Prime Directive–prohibited world. The Priam IV test, a Starfleet Academy holodeck training simulation of the 2350s, was set here, in which an escape pod from the USS Threnody crash-landed on Priam IV. (TNG novel: Survivors)

As this system has so far only appeared in a holodeck simulation, it might not necessarily be a "real" star system.
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