Apple ID payment method: vicious cycle - Can't add payment method in Apple ID until I validate my current method - but that is a card that I no longer have

I lost the credit card which was my payment method on Apple ID.

Now that I have a new card, I need to add this as my payment method.

When I try to add a payment method, I keep getting a message which says that I can not add a payment method until I validate my old one.

I can't validate my old one, since the card is no longer working.

I tried to remove that card, but I get a message that says "Unable to remove: Family organiser requires at least one payment on file". But, I am unable to add a payment method until I validate the old one, etc., etc.

Is there any way out of this vicious cycle??