Prefer to transfer only contacts from PC or Mac to your new iPhone without restoring from previous iPhone Tips & Tricks - Transfer only contacts to iPhonebackup?
This is how its done.
  1. Connect iPhone to iTunes on your PC or Mac.
  2. Click on INFO under Settings.
  3. Scroll down to ADVANCED option
  4. Select CONTACTS, click on Apply and Sync.
P.S – The above method works if you selected ‘Sync Contacts’ in ‘Info’ previously. On mac the contact would sync in Contacts app and on Windows PC it would sync in Outlook app.