Imagine you had the money to put into a nice young horse that had already completed a year of novice, was ready to move up but was super hot, a scopey jumper, a little tense and not super flashy on the flat, overall, an old fashioned event horse--leggy, gorgeous, but a little crazy.
To which rider would you send this horse? If you could send them anywhere in the US? And what would be the pros and cons of an UL rider vs a talented young rider/assistant trainer? In which region would this horse get the competition exposure it needed to either get sold or blossom into a nice event horse?
What are you sending the horse for - to get more training so you can ride it? To figure out if it's got big time talent, and will be the ride for a pro? To get it sold as fast as possible?How much money do you want to spend?
These are pretty different goals, and might require different folks. In general, if you're trying to get something sold fast, you want it with someone who will be competing down in Aiken or Ocala (East Coast) or California (West Coast) so the horse gets out this winter. For a sale horse, I'd send it to a professional who regularly has nice horses to sell and who will give it a polished, consistent ride. Boyd Martin, Jan Bynny, Sharon White come to mind as folks I think of who often have nice sale horses; Courtney Cooper often has more lower level horses and does alot of turnover on sale horses as well. I would not send a sale horse to an up and coming rider or assistant trainer unless you want to (at least in part) sponsor them on the ride - many of them won't necessarily show a horse to its best advantage nor will they have the connections to get something sold quickly. They will, however, in general be much cheaper. I don't think many ULRs take sales horses on a pure consignment basis, so the relevant day rate is pretty important.
If you're trying to improve the horse on the flat and/or make it a better ride over a longer period of time, I'd look to a rider who is very good on the flat. Allison Springer, Mara Dean, and Will Coleman are all folks I think of as having excellent flatwork and are good with youngsters; I don't know how much time/availability either have. Sinead Halpin is also very consistent, and I've loved the ride she's given to some horses who can be difficult on the flat.
I agree with what GotSpots says about being clear about your goals.
If you're planning/hoping to ride the horse again, I'd look for a rider who isn't so different from yourself. In my case, I'm a serious lightweight and a very quiet rider -- a large person or a strong, dictatorial rider would not be the right match for my horses if I planned to take over the ride.
If you want the horse to move up quickly to be sold, then send it to a pro who is successful with moving up and selling horses -- and be clear with them about your goals.
Christan Trainor, in a heartbeat. She has a knack for figuring out the hot, difficult ones, as well as giving the timid ones confidence. She also has a wonderful "natural horsemanship" type of trainer at her disposal (the wonderful Keith, who has put the manners, groundwork, and focus on Coda) to round out your pony's education.
She took my young guy from spooking at his own shadow to having him be the "old, experienced" horse in a group of greenies last weekend at a xc school - he's totally brave and bold now, but still very rideable. I highly recommend her for something like your pony.
"Opportunity is missed by most people because it is dressed in overalls and looks like work." - Thomas Edison
So, the Zen Buddhist says to the hotdog vendor, "Make me one with everything."
In addition to agreeing with much of what has been said, some other names that come to mind are Hilda Donahue who is soft and good with young horses, Doug Payne who is developing something of a reputation for being good with the tough TBy types, Debi Crowley is another who is great on the flat (though not eventing at the upper levels any more so you would want to keep that in mind)
Not Denny. He`s too old and too busted up!
There are quite a number of really good but still quite unknown younger riders out there, any one of whom can bring on a young horse to a certain point, and will do it much cheaper than some of the current BNRs.
But then you get to a different place, as it`s time for the horse to move beyond, say, preliminary. It`s good to have a "been there, done that" rider for the "green at the level" horse.
Carol Kozlowski in a heartbeat. She is great starting young horses and turning them out the correct way. Plus she is fair and consistent. The horses always know where they stand and what's being asked of them.
I would look for who is riding that kind of horse, or has in the past, and like others have said, can help you meet your goals, whether that be to give exposure and sell, or get training and retain.
Personally, I'd want to be in the area where my horse is, so I can get to my horse within a reasonable drive, to monitor and absorb training, showing experiences, etc.
On the west coast, Erin Kellerhouse would be tough to top. She's brought up (from BN) several upper level horses now competing with young riders/adult ammys. EXTREMELY patient and gentle. Horses fall in love with her.