Your current attorney will certainly have the right to charge at least for whatever time he or she has into the case. I do occasionally represent clients in fee disputes against their former lawyers. Judges and state bar fee disputes committees do try to be fair. However, judges and state bar dispute committees are generally willing to allow attorneys fairly high hourly rates for work they can document doing.
Depending on circumstances (how much you paid, what your lawyer has already done) you might get part of your fee back. It is unlikely you will get all of it back unless your lawyer is generous.