If your environment needs a strictly curated set of exercise and/or session templates, you should enable the environment setting Restrict Creating Exercise or Restrict Creating Session Templates in the Admin interface.

When enabled, only users with the Administrator role are able to create new exercises or session templates and change existing ones. Trainers can't add or edit exercises any more, they can however still use any exercise from the library for building workouts.
Any session template that was created by a trainer before this setting was enabled can still be edited and deleted by its creator.

Also, have a look at other environment settings.