Recently at PPM Works a customer asked if we could add a new tile for the Tasks Page to the App Launcher. Our initial response was to create a custom tile in Azure with a shortcut, but then one of my teammates found this helpful link.
You must be an Admin in the Office 365 Portal to be able to add a custom tile.
Tip: The image should be 60×60 pixels and be available to everyone in your organization.
Hope this helps! Please contact us with questions.