Hi Andre,
Sorry for late reply. This custom role was duplicated from Sales clerk role and we remove those role which require enterprise license. This role is mainly limit the user to perform Call Center order processing.
Due to licensing issue, the customer do not allow this role to edit the customer records, but they would like to allow the users to edit the address.
As you can see from the screen below, the role has a right to add new address, but the edit button was missing.

I also tried to add all the privilege related to addresses. But still no luck. Not sure what is missing here.