If you use iCloud or iTunes to back up your contacts, you can quickly bring them down to your iPhone in a matter of seconds.
The Steps from iCloud:
1. Launch the Settings app on your iPhone or iPad. 2. Tap on iCloud. 3. Turn On the option for Contacts — if it's already on, turn it off and then back on again to trigger a re-download. When asked what to do with existing contacts, choose the Delete option. 4. If you are asked, choose to Merge contacts. 5. Launch the Contacts app or the Phone app and verify your contacts are all there.
As I know you can do this without any problems in two ways: from ICloud ID for Web or from your iOS device. But remember that if contacts have been removed from iCloud, Apple allows you to restore them within 30 days. Here is good instruction for you osxtips.net/back-up-contacts-on-iphone/