Could ypu please explain and paraphrase the last part of the sentence.
The whole sentence: "Colin Firth gives a warm and sympathetic performance as Bertie, the Duke Of York, an introverted and uncomfortable stammerer, bullied by his father George V, played by Michael Gambon, and overshadowed by his charismatic playboy older brother, David, a role dispatched with some style by Guy Pearce, incidentally putting to rest the overpowering memory of Edward Fox in the part."
I assume this is about the movie "The King's Speech", although I can't even remember Guy Pearce being in that movie at all. The writer of this critique is confused as Pearce played the character of Prince / King Edward, not David.
In this context "dispatched" means "acted". To "dispatch" something can mean "to do it casually, and almost effortlessly," although there are only a few limited contexts where this doesn't sound odd.
She woke up early and dispatched her usual chores with such efficiency that she found she had the entire afternoon free.
Previously an actor named Edward Fox played the same character in a BBC series called "Edward & Mrs. Simpson", apparently so memorably that most people associated him with that role. However, apparently, Pearce acts so well in "The King's Speech" that the writer now thinks his is the better rendition.
