Does this sentence make sense?
They will be my new patients whom I never had a chance to care for since I volunteered at hospital.
It's a very awkward sentence, for sure. try this:
When I volunteered at the hospital, I never had a chance to care for __________. Now that I have my own practice, they will be my new patients.
You need to say who "they" are. The vagueness of this is part of the problem.