How to get my old contacts back

If your contacts are still in iCloud, just enable "Contacts" again in the iCloud setting on your new iPhone, after you finished the setup or restored form the latest backup of your old device.

Also check this article:

Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support

If necessary, try iCloud.com/Account Settings using a computer browser and go to Advanced at the bottom left. Access Restore Contacts.