How to transfer my AppleCare services from my old iPhone to a new one?

Transfer your AppleCare plan - Apple Support

If it was a replacement device:

"If we replace your device instead of repairing it, we’ll automatically transfer your plan to your new device. If transfer of coverage isn’t possible, we’ll offer other options."

If you returned one device and bought another you will need to cancel your plan and start a new one. Read this support article to learn how to cancel your AppleCare plan, or change the payment method —> Cancel or change the payment method for your AppleCare plan - Apple Support

You need to call 800-275-2273 and ask to be traansferred to the Applecare division. As far as I know, you cannot transfer the plan. You can cancel and get a prorated refund and then buy a new one for the new device. But, you can ask them.