How to Add Gmail Contact via iPhone
In the settings, set your default Contacts account to Gmail.


Launch Settings
Navigate to Mail, Contacts, Calendars
Scroll down to Contacts
Under default account, select the email address you use with Gmail.


Now whenever you create a contact on iOS, it will be added to Gmail. The only time a contact will not be added to Gmail is if you go into the Contacts application, select Groups on the top, and choose an account other than All Contacts or your Gmail account (e.g. iCloud).