You cannot enter a product key into a mobile Norton 360 product. Just signing into your Norton Account will pick up the active subscription and activate your product.
As I see no way to sign out of your Account from within the 360 product, go into Android Settings - Apps. Scroll to the 360 app and clear the app cache and app Data. Restart the device. This will reset your 360 to a trial version. To get the full version back, open the 360 app, then tap Sign In to log into your Norton Account. Enter your Norton Account information and you should have the full version again.