How to allow a user to edit certain Civi contact records without seeing others
There are a couple of different ways you can go about this.


One would be to grant access to CiviCRM, and the bare minimum WordPress access needed to actually get into CiviCRM.  You would remove the "View all CiviCRM contacts" permission from this role (also "Edit all CiviCRM contacts") and then they only have access to contacts based on their ACL.  This method gives the member access to the CiviCRM interface.
The second method is conjecture based on a similar technique I've used with Drupal Webform-CiviCRM integration - but I'm guessing you could use a contact reference widget on Caldera Forms CiviCRM to let a (privileged) member pull up and edit existing records.  This is a bit more work, but lets you limit the interface that the member sees to the relevant fields.


If you go with the first approach, consider the Contact Layout Editor extension to give the member(s) a more limited view of the CiviCRM interface, so they can't view/edit fields/tabs they ought not to.