I need to verify my new payment card

To verify your payment information, you need to -> Sign in to your Apple ID account page and edit / update your Apple ID details -> https://appleid.apple.com                                                     

• On the Sidebar click Payment methods -> then tap Payments Methods and tap Manage payment method.

Or see -> Add a payment method to your Apple ID

Add a payment method to your Apple ID – Apple Support (UK)

• If you want to change your card, you need to add first the new card, then remove the old card.
• or if you use your Apple Account balance, you need to set your Apple Account balance as your default payment.

If you update your payment method or add funds to your Apple Account balance, It would take about 1 to 3 business days in order to process.

If you're still unable to update your payment method, Contact Apple Support.

See also -> Payment methods you can use with your Apple ID

Payment methods you can use with your Apple ID – Apple Support (UK)

fyi: Not all credit & debit cards seem to work with App Store / iTunes Store, try a different one, or preferably a credit card.

If your card is not accepted as a paymenf method, you need to contact your bank.

Get more help and assistant from Apple directly, see Contact Apple for support and service -> Contact Apple for support and service – Apple Support (UK)