If you use Outlook Web Access (aka OWA, aka Outlook on the Web) and a modern browser (Google Chrome, Microsoft Edge) you can now enable Desktop Notification to get notified when emails arrive while you are no longer browsing your mailbox but your browser is still running.
To turn it on, logon to your mailbox using your favourite browser (https://outlook.office.com/) and access the (quick) Settings menu available on the left side of your picture
Then you can turn on the Desktop Notification
After turning the option on, you may get a prompt from your browser asking confirmation to allow outlook.office.com to Show notifications
You will get a confirmation of the successful activation
You can also enable/disable it from the (complete) Settings under the General section
Then next time you have your browser open but not your mailbox and email arrives, you will get notified on your Desktop