Old iPhone data

If you have transferred the data from the old iPhone to the new one and deleted the data from the old iPhone all your data will get deleted from the new iPhone too.

1. Sign Out from iMessage and face time
2. If you purchased an AppleCare plan for your device, cancel your AppleCare plan.
3. If you paired an Apple Watch with your iPhone, unpair your Apple Watch.
4. Sign Out from iCloud / Apple ID

Now you can delete the data from the Old iPhone. All the data on new iPhone will remain.

Are you asking how to ensure that all your files and information have been deleted from your old iPhone so that it is safe for you to sell it or trade it in? If so, try this link:

What to do before you sell, give away or trade in your iPhone or iPad – Apple Support (UK)