How do I restore my contacts to my iPhone 6S from iCloud

If you were using iCloud to sync your contacts, go to Settings>Your Name>iCloud>Apps using iCloud>Contacts>On. The contacts should sync to your phone.

If you weren’t syncing contacts with iCloud but were including them in your backup, you have to restore the backup to recover your contacts. When you restore a backup, you overwrite the contents of your device with the content in the backup.

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

If you synced them to iCloud, they should populate your iPhone when you sign in using your Apple ID.

Regards

Giulio