Option 1: update the existing GDPR notice for that very form to include the partner name and perhaps a link to their privacy policy. This way, you don't have to create anything new, you just combine the legal wording around it and people only have to tick one box.
Option 2: You can add a custom property that's with a checkbox type and use that for this specific occasion.
I guess, it depends on whether you want to be able to identify who has clicked on which button or just to be compliant overall.