Are you looking to put the horse in full time training or just take lessons with a few Pro rides? Can take longer to change a horses style then teach it in the first place. May also be some conformation angles that just don’t allow a tighter, cleaner jump.
Would make sense to have whoever you are thinking of selecting do an honest evaluation ( for a fee) and explain their plan for the horse going forward. “Oh, sure I can fix that” without really evaluating the horse in person, in the irons can be an empty promise. Beware. Even “ the best” cant fix everything. Plus there is a financial component for most owners looking for a trainer.
Thing with “ the best” is it doesn’t do you much good if they only take full service board, full training clients at 3k a month and you cant do that and/or head trainer is on the road competing, not at home training anyway.
Can you share more general information on what you are looking for, no need for specifics. Just a general idea what you expect from trainer, full time board and training or just some help.