Lost contacts on phone how to recover

If your contacts are sync'd to iCloud or to your chosen email provider (ie the usual method) then they were not backed up. Nothing sync'd to any cloud is backed up conventionally.

• If they are sync'd to iCloud then try this 

Use iCloud.com to restore and recover iCloud information – Apple Support (UK)

• If sync'd to email provider eg Google then contact the provider for help.

Finally if you are one of the rare people who have their contacts on the phone only then you can wipe the phone and restore from the backup, but you will lose everything since the last backup.