How do I hide Primary address label for partner profile for non-admin layouts?

You can follow these steps to hide Primary address label for partner profile for non-admin layouts:

1. Remove the conditions and change the order of the current layout to hide the address label for the admin user using Page Composer.
2. Make another layout visible to the admin user. This ensures that the other layout is the first to match the admin user conditions.
3. Configure using Application Composer and assign Conditions to Page Layouts.

This way, the address labels will be hidden for all non-admin users.