This will wildly depend on which version of Outlook you are using. 

Classic Outlook - the shared mailbox should automatically appear if you are assigned to it. 

New Outlook - you may need to manually open the shared mailbox.

Outlook on the Web (browser) - you will need to manually open the shared mailbox. 

For step by step instructions:

Outlook for Mac - you will need to manually open the shared mailbox. 

For step by step instructions:
https://support.microsoft.com/en-us/office/open-a-shared-mail-calendar-or-people-folder-in-outlook-for-mac-6ecc39c5-5577-4a1d-b18c-bbdc92972cb2