Its good overall. It's specific, gives a good hook, and lets audience know exactly what they're getting into.
I think there're a few grammar issues and redundancies. "Taking the place of the murdered prince in this world" in the second P is redundant since you already said it in the first P. There needs to be a "with" before "a murderer on the loose." In general, replace loose terms like "get to" with something more specific.
"enthronement as king" is awkward, but I cant think of a better term for it right now
How I would rewrite it:
After his sudden death, Jon finds himself in the body of prince Zephyr who had been murdered on the day of his enthronement as king. Now Jon is stuck with ruling a kingdom while "his" murderer is on the loose! Determined not to let his life slip away a second time, he decides to track down the murderer before they can get to him. Will he succeed and survive as a king in this world?'
You could certainly spice it up more i.e "ruling of a kingdom" could be "with the weight of the crown on his head" etc etc