What are the laws or standards surrounding personal trainers with your organization recommending supplements to their clients
The personal trainer would need to refer to the code of ethics of the organization that they are certified by. Each certification body has their own code of ethics.
As fitness professionals we have a scope of practice, the scope of practice delineates what is within and outside of our professionals.
It is not within the scope of practice of fitness professionals to recommend supplements.
Best to you.