BuddyPress.org

You would need to modify the profile loop template so only BP site admins can edit the profile field in question.

Get acquainted with the profile loop:
https://codex.buddypress.org/developer-docs/custom-buddypress-loops/the-profile-data-loop-bp_has_profile/

Which you can modify in your BuddyPress theme’s /members/single/profile/edit.php file.

You can use `is_super_admin()` to check if the logged in user is the admin.