Within Teamwork Projects you may want to grant task list template access to some of your users. This will allow them

Note: Only the site owner or site admins can grant access to these users.

First you will need to navigate to the people section of your site:

You will then be able to select the user from the list. Once you have done this choose the green 'edit' option to the top left of the user page:

You will be presented with a new window, choose the 'Permissions' tab first and you will then have the option to toggle on 'Can this user manage task templates':

When you have toggled this on or off, remember to select the green 'Update' option to the bottom of the box.

Once this has been enabled for the user they will then be able to access templates from the dropdown arrow to the left of the task list name:

Note: Once you enable this permission it will allow template access for all projects the user has access to.

For more information see: Managing user profile permissions