Phone Contacts

Contacts are neither stored locally on an iPhone nor in SIM. They are synced to an email account that you had Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other

If Contacts on iCloud, try this --> Restore contacts, calendars, bookmarks and more using ...

1. How many Contacts account (email client server) you have?
2. What is your default Contacts Account?
3. Which email account you are using to store Contacts?

• See the GIF below for Contacts and Default Account

• Learn how to add an email account and make it default (Watch the GIF)
• This example is for Gmail but the process remains same for all Google, iCloud, AOL, Exchange, Outlook, Yahoo or any Other

iCloud backup doesn’t include information that is synced and stored in iCloud, like Contacts, Calendars, Bookmarks, Mail, Notes, Voice Memos, Messages*, shared photos, iCloud Photos*, Health data, call history, and files you store in iCloud Drive.

*-If you had turned on Messages in iCloud & iCloud Photos, your content is automatically stored in iCloud. 

Check Settings, Contacts, Accounts

Do you have other accounts there with Contacts turned on (green)