Unfortunately it is not possible to "conditionally" limit the edit permissions for a field. What you can do is limit specifically what users can update, by right clicking on the field and selecting Field Permissions.
As a workaround, I guess you could have your team working form an interface. Within an interface you can play with visibility rules (see Rules on image below) to determine whether the field should be visible or not, and hide it if it is not empty (or other conditions). Even if hidden, you can show it elsewhere as a calculated (e.g. formula) field which is not editable.
