1.Back up your iPhone to iCloud including contacts
2. Tap on Settings > Contacts > Accounts.
3. You will see your accounts here. Tap on iCloud. Scroll down and switch OFF Contacts. It will say Keep on my iPhone or Delete from my iPhone. Choose Delete from my iPhone.
4. Next step is to re-enable the Contacts to ON here.
5. If it says Merge contacts, Confirm and proceed.
6. Restart your phone and try
Hopefully this works for you. Good Luck