I understand that you're missing contacts after upgrading to a new iPhone, and I'm happy to help. If you have an iCloud or iTunes backup of the old phone, you can try restoring a backup to the new device:
Restore your iPhone, iPad, or iPod touch from a backup
If you're still in possession of the old phone with all of its data present, you can back it up and use the instructions above to restore that backup to the device.
How to back up your iPhone, iPad, and iPod touch
It's possible that your contacts were synced with an email account that was on your old device. If that's the case, you can try adding that email account to the iPhone:
Set up an email account on your iPhone, iPad, or iPod touch
If you were using iCloud to sync your contacts, these instructions may be helpful:
Get help using iCloud Contacts, Calendars, or Reminders