Within Teamwork.com, you can grant task list template access to individual standard users on your site.
Note: Client users and collaborators cannot be granted task template permissions.
Users with permission to manage
task templates can access, manage, and save templates via the options menu in the project's List area or via an individual task list's options menu.
Click the More option in the main navigation menu and select People from the pop-out menu.
In the People area, go to the People subsection.

Select the relevant user from the list to open their profile. In the top right of the user's profile, select the Edit option.

In the edit details modal, go to the Permissions tab and toggle on Can this user manage task templates.

Click Update in the bottom right to save the changes to the user's permissions.
Note: Only the site owner or site administrators can manage user profile permissions.
Once this has been enabled for the user, they will then be able to access templates via the task list options menu in either Table or List view on a project.

Task list template options
Once you enable this permission it will allow template access at project level for all projects where the user is a member.
- Manage task templates - gives the user access to the Task Templates subsection of the site-level Templates area.
- Note: The user will not be able to access other sections of Templates or other site settings.
- Add tasks from template - allows the user to add tasks to the task list from an existing template.
- Save as template - allows the user to save an existing task list as a template.
For more information, see: Managing User Profile Permissions