On iPhones and iPads, it's pretty simple to take backups. In fact, iTunes does it for you, check: Back up and restore your iPhone, iPad, or iPod touch with iCloud or iTunes - Apple Support
If you haven't got a backup, and forgot to take iTunes backups (because you hadn't synced your iPhone to your PC), you need to consider alternative solutions, by going through their websites and reviews.
Actually, when we delete a contact from iPhone, the contact doesn't get deleted really, it still stay somewhere on our phone but is difficultly detected by our eyes. It's because the deleted data is technically marked for deletion by the operating system and hidden so that they become invisible to us.
Do you know how to restore contacts on iphone? As is known to us, when we have no previous backup to restore, the only way to retrieve deleted contacts on iPhone is by using a third-party tool.