There are multiple ways of troubleshooting when your mail app is not updating, here’s a guide on how to solve the issue.
Usually, the issue is found in the Mail client not fully downloading an email from the server and thus it cannot be displayed properly.
Open up the “Settings” app and go to “Wi-Fi”, then check whether you are connected to the right network by examining the ticked-off entry in the list.
Next on our list, if the above failed, would be to restart the Mail app on your i Phone hwne your Apple mail is not uating.
Check your internet connection by going to a random website in Safari and tapping a link to see if it loads.
If that works, you can rule out a connection problem between your i Phone and the internet, but your mail service might be having issues.