The "New Outlook" is not recommended at this time as some functionality is still missing. See Feature comparison between new Outlook and classic Outlook for a feature comparison.
To access a Departmental/Shared mailbox that you have permission to:
It may already be available for you in the New Outlook. To see it, scroll to the bottom of your mail folders and expand the folder called Shared with me:
If it isn't there, right click on your account name at the top of the folder listing and select Add shared folder or mailbox to open it:
Enter the email address of the shared mailbox and click Add:
The mailbox will be added under Shared with me:
