The domain ranking will not pass to the subdomain. The subdomain is treated like a separate website. This means that if you get ten backlinks to your main site. The subdomain will still have zero backlinks. I would not create a different website either for your trainers. Your new trainers would start with a domain and page rank of zero. I suggest that you add your trainers to the following:

website.com/trainer/trainersite

This way, the trainers will be able to get the domain rank of the main website since it is a subfolder.