Email can be removed from your mail server to keep your email storage down (to stay within quota).
This can be done by changing the setting in Outlook (a similar setting can be found in your iPhone/Android email settings), to delete email from the server when it becomes 7 days old.
First, ensure your account is configured as POP (if this says IMAP, you’ll need to backup your email and re-add the account as a POP account):
You’ll find “Remove from server” settings in “More Settings” when you edit your account.
This setting won’t delete email from your PC, only from the remote server.