I don't know the length of this; it's probably more than a short story, but it may only be a novelette. I read this more than 20 years ago, but based on the feel it was probably a much older story. Might have been in an anthology, but I can't recall which.
The protagonist is a noble of some sort (not a prince, I don't think, but his father was planetary leader) in a galactic space-traveling milieu. I think at one point he travels off-planet to find his brother. They have to be very careful, and they can't trust anyone, because the alien has taken over so quickly and successfully by telepathically detecting people who would resist it, and I think by inducing a kind of loyalty.
What I most clearly recall are the human puppets of the alien; when the alien is finally defeated it is discovered that the guy had appeared hunchbacked because of a giant alien growth on his back that was how he was being controlled. The female consort, who was the attractive face of the junta, had the alien growth on her front (replacing her breasts and abdomen). They both die when the alien is killed; the alien tissue in/on their bodies dies with it and that kills them.
The story feels old because of the idea of a planet being governed by a hereditary ruler and the fact that the hero is the heir seems very "Golden Age" to me.