There's a pro showjumper who visits my livery yard fairly regularly for clinics etc who offers this as a service which I and many others on the yard have used for breaking-in, re-starting after a break, re-schooling problem ones, the more serious competitive riders have had him ride and compete their SJers for them for periods of time for whatever reason. I can only speak from my own experience of this one yard, it may be different elsewhere.
It's expensive: £275 p/w when I last used him and that was a few years ago now, I expect he's put his prices up since then. He does fully care for your horse inc all food and bedding for that price but obvs if you still need to pay to keep your livery space/stable at current yard it's quite painful. If it's a breaking-in or restart type arrangement he would expect to keep them 6-8ish weeks, anything else it obviously depends what you want but he's reasonably good at giving you a timeframe - I would def recommend talking this through honestly at the start, what your goals and expectations are and getting them to give you a clear estimate (obviously understanding they won't know for sure until they start working with the horse but they should be able to tell you if what you're asking for is reasonable for how long you want them there).
What you get for that price: an initial assessment of your horse (which for me included him watching me ride at home then him riding on arrival at his yard) followed by a long conversation about his plan and goals etc, then weekly whatsapp/email updates (sometimes these were just a few pics and 'going well', sometimes more detailed). He schools your horse once or twice a week himself and a further 3-4 times a week your horse is schooled by his working pupil/yard girls (who are all excellent riders btw) working to his plan, or lunged or hand walked or ground work by them as needed. For the more competitive types he may take them on outings to shows or XC schooling/arena hires himself (or the working pupil will) if there's space on the lorry, mine were never considered smart enough to be seen publicly under him name sadly 
. He also encourages you to come to his yard at least a couple of times while your horse is with him to ride yourself under his eye, he doesn't give you a lesson as such but kind of watches to see if what he's been working on is translating to the owner riding, which while very intimidating pootering around on my little scruffy beasts at his very smart facility, weaving around his 1.20 'schooling' jumps and with an audience of the said very excellent/talented girls watching on 
, it is worth it, I'd look for someone who offers/encourages this.
Pro riders can tend to ride in a very different style, mine isn't forceful to the point of being unkind but he's certainly a lot firmer and has higher expectations of the horse than I ever would, I have seen it happen where the horse is going beautifully at his place but once back with their owner goes backward rapidly, can be really confusing for them to go from one system of near-perfect consistent riding to back with a bumbly/nervous/overly gentle rider (including myself in that!) so with the 'problem' ones it can almost make them worse than when they started so that's something to watch out for. You want a pro that 'gets' your style of riding and what you use the horse for and matches that as far as possible... e.g. mine is used to showjumpers so getting them hacking well isn't a particular priority, if it was hacking issues I was looking for help with I think I'd choose someone else...