I still have Apple Care on my old I Phone that I traded in at Apple for my new I Phone 13, can I transfer the care to my new ophone?

No, but you can cancel the AppleCare+ on the old phone and get a refund if you have time left on it and then purchase AppleCare+ for the new phone. See→Cancel or change the payment method for your AppleCare plan - Apple Support

Verizon did a warranty replacement on my iPhone 12 Pro. So Apple care + didn’t transfer like it did when best buy replaced a previous one. Apple DID transfer the plan to my new device. It took then an hour and 20 minutes, and now cancelling the remainder of plan has become a nightmare. But it can be done. Maybe shouldn’t be done based on my still going experience