Sync Gmail Contacts With Your Mac Device
Follow the process below:
Open the Settings app on your device.
Select Mail, Contacts, Calendars.
Select Add Account....
Select Add CardDAV Account.
Fill out your account information in the following fields:
Server: Enter "google.com"
User Name: Enter your full Google Account or Google Apps email address.
Password: Your Google Account or Google Apps password. (If you’ve enabled 2 Step verification, you’ll need to generate and enter an application specific password.)
Description: Enter a description of the account (e.g. Personal Contacts).
Select Next at the top of your screen.
Make sure that the "Contacts" option is turned ON.
After you've completed setup, open the Contacts app on your device, and syncing will automatically begin.