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Starmie is just too fast naturally to efficiently make use of Trick Room without getting outsped by things that would normally underspeed it. And these things are generally very bulky. Especially since im assuming you won't be able to minimize it's speed as much as possible since it's an ingame one. Your best bet is a bit of bulk, max sp.atk, and maybe an AV.
Though if you really wanna try for a Trick Room set, go on ahead! Who knows? The sheer surprise factor could catch people off guard, and I think Starmie itself learns Trick Room, no? It could be pretty neat against offensive teams due to their speediness and Starmies coverage. Try it out if you're reaallly feelin it. Personally, I think Quiet Starmie is a bit of an unfortunate setting but hey maybe you can make it work?