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.

Domain advantage will not be passed on to the subdomain. Google will treat the subdomain as a different website.
If you want to pass site juice to the trainer pages, then set it up as normal pages, like:
domainname.com/trainername
domainname.com/trainername

Buying new sites for all trainers will not pass domain juice. I hope this helps. In case of further help with SEO, email me at varun@upreports.com

Hi there,

I recommend to use sub directory if you want to take the SEO advantage.

In sub domain, authority & link juice will not pass and Google treat every sub domain as a separate entity.

I hope this helps.

Thanks,
Hiren

A subdomain will be seen as a separate website by Google, so you might as well create a different website for every trainer and link to it from the main website to give them a DA boost.