How to retrieve deleted contacts from past backups

If you still have the backup from years ago, and it would have to be on a computer, then you would have to erase all content and settings (ie wipe the phone) then restore it from the old backup.

You first need to make a new backup in a separate location so as not to override the old backup. Then after retrieving the photos and storing off the phone, restore the new backup in the same way.

A lengthy process!

It is unlkely that contacts were backed up unless your contacts were only on the phone, rare because most people store contacts in a cloud account such as iCloud or Hotmail or Google Contacts etc.