If you are using an iPhone and your Gmail not working on iPhone then you can resolve this problem.
First, Make sure your cellular data or WIFI should be turn On.
Restart your iPhone
Open Gmail website to check Alerts.
Check The Storage space of Gmail.
Make sure IMAP is enabled.
For that, Go to the web browser and sign in to your Gmail account.
Go to settings on the right side of Gmail and select all settings.
After that, select Forwarding and POP/IMAP > Enable IMAP > Click on Save changes button.