Yes, tell you trainer that you'd like to buy a horse. They know you ability level, will have an idea of the type of horse you'll need, and have been around the block when it comes to purchases.
They can tell if a horse has poor training, is over priced, predispositions for health problems, suited for your body type, any number of things. They may also know of horses who are not on the market that would work.
Or they might say you are not ready and may suggest a lease instead.
I don't know of any trainers that wouldn't teach you on your own horse. There shouldn't be any reason you can't continue your lessons as is.