It's an interesting challenge you've been given - " Improve the supplier that doesn't want to improve ". I've been asked to do that before.
As for compelling them to have a Quality person, that's not usually a solution. I've both had suppliers and worked with employers who assigned their top "excuses" guy to wear the Quality hat, and many sad things were witnessed.
As [silentmonkey] said, "how does your organisation handle poorly performing suppliers?"
Sometimes your organization has no willingness to disqualify a supplier - in that case all you can do is document the supplier's shortcomings, endeavor to get them to improve, then report that the supplier doesn't want to improve. It's an exercise in futility, but it needs to be on the record.