If you are running out of space, or if your mailbox/archive is full, you can follow these steps to clear up some space:
In Outlook, right-click on the Deleted Items folder and select Empty Folder.
Click Yes on the prompt that appears.
If this didn't work, you can go into other folders (Inbox, sent items) and delete older, unwanted emails from those which should free up a lot of space.
If it is the Archive mailbox that is full, you can click on the Online Archive on the left and follow the steps above to clear out space in those.
If you require further assistance, please raise a new case online and reference the title of this article. Please also leave behind the following information:
Who is the user experiencing this error?
Is it mailbox that is full, or archive?
A screenshot of the error/notification that appears.