Phew. Tough question.
I have the feeling that expats in Hamburg (most of them) blend in quite quickly, not like Munich where many of them stick mainly with the expats and even after many years of living in Germany don't speak much German. So if you are looking for a job where you mainly talk to people, this is going to be a challenge.
Do you have a licence to work as a therapist in Germany? That would help.
In Germany pretty everybody can work as a therapist, but if you have a licence (as in licence so that Krankenkassen/health insurance companies will pay your fees), it is much easier to find customers/patients. If you don't have such a licence people will have to pay out of their own pockets, and that makes it harder to find customers.
For a start (apart form all the paperwork with the officials, and sorry, I don't know who you would have to contact) you could contact self-help groups, there might be some with professional (paid) therapists, or that can give you at least some contacts.
There's an organisation called
KISS - they are kind of a union of self help groups, supported by the state, I think they do have some groups in English and they also work with hospitals and rehab clinics.
A couple we are good friends with work in a rehab clinic, I will ask them if they have any more ideas.
Maybe you do some googling for "Hamburg Therapie Englisch" - or "Hamburg Selbshilfegruppen Englisch".
Good luck - and welcome to Hamburg