Hi @Mark McIntosh ,
Currently new Outlook doesn't support the option "Add Shared Mailboxs to Favorites", and the development team is planning to support this feature in a future update.
Microsoft has collected this feedback and you can vote through this link:
https://feedbackportal.microsoft.com/feedback/idea/f8c3dc39-78bd-ed11-83ff-000d3a1ab7d1
Many features of our current products are designed and upgraded based on customers’ feedback. With requirements like this increase, the problem may well be released in the future.
You can mark my reply as an answer, so that other users in the forum who have similar problems can also vote.
Note: Please follow the steps in our documentation to enable e-mail notifications if you want to receive the related email notification for this thread.