Restore my contacts on my iPhone

If you weren't syncing Contacts with iCloud, do you have a backup you can restore from? Restoring from a backup erases all data currently on your device. Any data newer than when the backup was made will be erased. A restore is an all or nothing restore. You can't access a backup to see the contents and only restore certain files.

Backup - Restore your device from an iCloud or iTunes backup.    *

https://www.youtube.com/watch?v=_VNsH_OWmRw

https://www.youtube.com/watch?v=Jbp3gGTQygg

If you were syncing Contacts with iCloud, go to iCloud.com/Account Settings using a browser and under Advanced at the lower left, select Restore Contacts.