Outlook via the Office 365 Home

When you log in to Office 365, you will be able see all of the applications that are included in your subscription plan. 

From the Office 365 Home, you can click on the Outlook icon to go to Outlook:

You can also right-click on the Outlook icon and choose Open in new tab, Open in new window, or Open in new InPrivate window from the drop-down:

In IE, Chrome, Firefox, and Edge, you should at least have the choice to Open in a new tab. If you do not have this choice, you may want to check with your admin. The other choices may depend on your browser.