There are two ways, one is the long road that any service has taken to get recognized by health insurance companies. This takes decades, state (and some times national) licensing, mounds of empirical evidence suggesting that exercise led by a Personal Trainer is significantly more effective than without, as well as a nation wide agreed curriculum for teaching and training fitness professionals.
Option two, a long shot, the individual needs a doctors “prescription” that the only reasonable and effective way to treat the patient is through personal trainer instructed exercise. This might even have to be prescribed by more than one doctor, second opinion, before the insurance company will begin to think about reimbursement.
You might try contacting insurance companies to see if you could be listed as an alternative or preventive health care. I worked for a massage therapy wellness center that did this with Blue Cross Blue Shield and in return they gave BCBS customers a 20% discount.