Without writing a custom plugin, I think your best bets would be to either:
1) use something like gravity forms and have the user start as subscriber, but then enter request to be a partner (using a GF form). GF can send notifications on forms to admin. Admin then upgrades the user’s role.
2) use a interim role like “request to be partner”. New users get notified to admin.
“request for partner” users reviewed and upgrade to “partner”.
Do editors by default have capability to manage users ? I suspect maybe not. In which case you could use a role manager plugin (justin tadlock members plugin for eg) to add manage_users to the editor role (which would probably mean an editor could make themselves an Admin? hmm maybe not a good idea? ….)