If you want to recover your iPhone contacts, you can recover contacts directly from the iPhone and to retrieve previous contats by extracting it from iTunes backup.
You can extract your contacts from the iTunes backup when you lost your iPhone. iTunes can automatically back up your iPhone contacts and update it every time when you sync it. So you really have a big chance to recover contacts from iTunes backup.
Let's check how to recover contacts with or without your iPhone
Part 1: Directly scan and recover contacts from iPhone (with iPhone 5/4S/4/3GS)
Part 2: Scan and extract iTunes backup to recover iPhone contacts (without iPhone)
Part 1: Directly scan and recover contacts from iPhone 5/4S/4/3GS
Step 1: Connect your iPhone to the computer
Step 2: Enter the device's scanning mode and scan it
1) Hold your device and click the "Start" button.
2) Pressing the "Power" and "Home" buttons at the same time for exact 10 seconds.
3) Then release the "Power" button, but keep holding "Home" for another 15 seconds until you get the message of successfully entering.
Whatever the device you use, the program will automatically begin scanning your iPhone for lost contacts after you doing the steps accordingly.
Step 3: Preview and recover iPhone contacts
When the scan is finished, you can preview all found data before recovery. Choose "Contacts" to preview, mark it and click "Recover", you can save all the contents on your computer with one click.
Part 2: Extract iTunes backup to recover iPhone contacts
Step 1: Scan the backup file
Step 2: Recover your iPhone contacts
How iTunes backs up your iPhone contacts
As an iPhone user, who tends to manage the content of iPhone with iTunes, must know that iTunes backs up everything of your iPhone first when you sync with it. This will be the warmest thing when you lost your contacts from iPhone. The bad point is that the backup file is not regular file type, but a SQlitedb file, which is not allowed to preview, even access. Sometimes it's encrypted, just for private safe.
You can read the detailed steps here:
How to Recover iPhone Contacts
I hope it can help you. Good luck!