exchange old iphone for a new one

You need to sell your existing phone privately, then use the proceeds from the sale to partially offset the purchase price of a new one.

Depending on the model and condition of your old phone, you can take to your local Apple store and perhaps receive a credit for it on the spot. There are also online sites that will provide you with an estimate and a check to follow after they actually receive and inspect the old phone. Just be sure to do a back-up to iTunes before it leaves your hands so you can get the new one up to speed quickly. If you want to restore health data onto the new phone, you'll need to specify an encrypted backup.

Apple will give you minimal credit for ANY phone as they really have no use for used phones. They will give you some $$ as part of a recycling initiative. It is always better to sell it and use the proceeds towards the purchase. You probably will get a better value that way.