When setting up a new Email account in your Microsoft Outlook (or similar) you must ensure that emails are not stored on the server indefinitely or you will eventually run out of hosted space. Typically in your Email account settings, “More Settings”, “Advanced” tab, see “Delivery” – “Leave a copy of message on the Server” – make sure this is set to less than 14 days or unchecked completely. This does not affect emails on your computer, only how long it keeps a copy on the hosting server.
Firstly, make sure those settings have been changed so it doesn’t happen again.
If you are not confident with making changes to email accounts or deleting files from your cPanel, please ask an IT friend to assist you.
Then delete the excess old emails from the server by logging in to your cPanel, navigate to “Files”, “File Manager” and make sure to select “Show Hidden Files (dot files)” before going into the File Manager. Then navigate to your “mail” folder, then view each account to find where excess files are being stored and delete excess/older files, which are typically in the “cur” folder of each account.