You can share your own templates only with your own group or with all the users in your account irrespective of which group they belong to.
In other words, a user cannot share its own existing Library Template with another specific Group. For example, user A from HR group cannot share its existing Library template with user B from IT group.
For more information on change Templates permission, visit the following link:
https://helpx.adobe.com/sign/help/change-library-template-permissions.html