In the control panel for groups - when you are editing a group, there is the option to Link Roles - and the documentation says:

Linked Roles – These roles are automatically generated. Users who join the group will be added to these roles. The roles can be used to control permissions for the forums and other parts of your website.

But it doesn't seem to work - I linked a role to my premium role for paid users in a public group, and then went and joined the group as a registered but non-premium user, and nothing happened - I can't access the premium content, and the user account did not get the roles added. That user is in the group, and has access to all the group stuff, but I cannot see any evidence that the link roles did anything.

Does the role need to be a new role just for use with AS? as in it can't be an existing role or something?

I like the idea of linking roles as it gives me a way to offer a free premium account to someone if they join certain groups.

The name is misleading. While it does allow you to add a role that is not the intended purpose.