Although you will need to contact your insurance for more information, I believe that you will not be covered. Each country is governed by their own laws and regulations, they have their own legal system and if anything was going to happen that would hold you liable, neither the client there nor the insurance here would have any jurisdiction in a court of law (on either country). For that reason I would seek a liability insurance in Germany or one that covers fitness professionals within the EU. This might require you to get certified by one of the fitness certifications which are accepted there. Good luck!
this may also depend on the capacity in which you will work in Germany. If you were to work for the American Embassy or maybe the Armed forces, you may still be ‘on American soil’, and yet another set of rules may apply.
But if you just work in Germany, you will very likely need different insurance coverage.