How do I set up my Apple Card on a new device, so that I am able to make payments to my Apple Card automatically? I am using a new device and need to add the card to my new device.

Are you using the same Apple ID on the new device that you used to apply for the card? You can make payments at card.apple.com and you can:

Set up scheduled payments for Apple Card

1. Open the Wallet app on your iPhone and tap Apple Card.
2. Tap the more button , tap Scheduled Payments, then tap Continue.
3. Tap Pay My Bill to pay your previous monthly balance or tap Pay Different Amount to choose an amount. Then tap next:

• • If you chose Pay My Bill, select when you want your payment to be made, then tap Next.
  • If you chose Pay Different Amount, select your payment amount, when you want the payment to repeat, when you want the first payment to be made, then tap Next.

1. Confirm with Face ID, Touch ID, or passcode.
2. Tap Done.

If you want to change your scheduled payment, you need to first cancel your current scheduled payment. Just tap the more button , then tap your scheduled payment under Scheduled Payments. Tap Cancel Payments and tap Cancel Payments again to confirm your choice.

but pay the card automatically.

See instructions in: How to add Apple Card to your Apple devices - Apple Support

read my post - you must be using the same Apple ID you used to apply for the card with.

You can make payments by going to card.apple.com

You cannot add the card to a phone with a different Apple ID. You will have to close that account and apply using the new Apple ID.