On your iPhone, open Settings
Tap Contacts
Tap Accounts
Tap Add Account
Tap Google
Sign in with your Google account
Turn on Contacts
Tap Save
Open the Contacts app to confirm the contacts synced
If contacts do not appear, go to Settings
Tap Contacts
Tap Accounts
Tap Gmail or Google account
Make sure Contacts is enabled
Pull down in the Contacts app to refresh the list