Solutions for iPhone users

from How to Fix Apple Mail Not Syncing with Gmail Problem

Fix 1: Restart your device

Ninety percent of problems can be solved by rebooting your device. Some unknown errors on your iPhone may be the culprit of the Gmail account not syncing with Mac mail problem. So what you need to do is simply restart it, and check your mail to see if the issue is fixed.

Fix 2: Check out the Push Setting

The wrong Push setting is a minor that can create the synchronizing issue. Many users don't know that they should manually activate it to start the synchronization of emails. So, if you were not aware of it, it's not too late now.

1.Open Settings on your device.

2.Navigate to Mail > Accounts.

3.Tap on Fetch New Data, and tap on your Gmail account.

4.Enable the Fetch option for Gmail, and make sure the Automatically option is checked under the Fetch section.

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How to Fix Apple Mail Not Syncing with Gmail Problem