You can grant the Read/Manage permission on your managed public address books to specific users, groups or memberships.
A user with the Read permission can see the address book.
A user with the Manage permission can view/edit/rename and manage permissions on the address book.
By default, any member of a group has the Read permission and the group manager has the Manage permission.
Grant a permission on a public address book
1. Right-click your managed public address book, and select Permission from the drop-down menu.
The Permissions form appears.

2. Select certain users or groups you want to grant permissions. For more details, see here.
3. Tick the Can manage? checkbox if you want to grant the Manage permission to your selected users/group.