If you want to understand more about the user roles in Timetastic then have a skim through this article: Access & privacy - who can see what.
Making someone an admin user
Click USERS from the main menu, and use the options menu on the right hand side of each employee to add/remove admin status.
The 'Make admin' option is only available for users with a registered email address.
You can easily see your admins on your Users page as they are circled in yellow with a tick icon:
Removing an admin user
It's the exact opposite, head over to the same place and you'll see the link changes to 'Remove admin'.