Outlook Add-ins: Can we have a new event that trigger if any new email received in mailbox

The endpoint to process change notification and lifecycle responses from Graph must be publicly accessible in your Web API. You cannot receive these in web pages that are loaded from client-side processes like an add-in task pane. After your Web API processes these responses, you can then read or manipulate the affected Outlook items (e.g. apply categories, flags, move emails to folders, etc.). However, if your add-in needs to interact with the affected items, you will need to send a request to your Web API from the add-in and have it return whatever data you need or do something else.