How to switch an Apple Card from one iCloud account to another

The Apple card is tied to the Apple ID used when applying for the card.

See if anything here helps.

Set up Apple Card Family and add a co-owner and participants - Apple Support.  *

It is virtually impossible. I was told that I had to close the original account and reapply using the new Apple ID. So I closed the account and reapplied. Although Apple card specialists told me repeatedly that the application was being reviewed, I received an email a month later stating the application could not be processed due to a system issue and that I should reapply. I again applied, and a month later received another email stating the application could not be processed due to a system issue. I just reapplied again, but I doubt that it will work this time either.