To sync your Google contacts with your Apple device like iPhone, iPad, iPod touch, Mac. we recommend using Card DAV, which is an Internet open standard. When you sync your Google contacts using Card DAV, you’ll be able to edit, add, and remove contacts from your device and keep them in sync everywhere you use them. Call us at 1-866-324-3042 for third party Gmail customer service or visit http://www.gmailcustomerservice.us
If you use Google Apps for Business, you can use Google Sync to sync your contacts to your iOS device.
Sync your contacts
iOS 7+ Open the Settings app on your device. Select Mail, Contacts, Calendars. Select Add Account. Select Google. Fill out your account information in the following fields: Name: Enter your name 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".