Using the New Outlook for Mac for personal email and calendar
What type of email account do you have configured in Outlook? POP, IMAP, Outlook.com, or Microsoft Exchange?
Can you find the messages using search?
If using IMAP or a Microsoft Exchange account, are the missing messages still on the server?
Were you using the On My Computer folders for the messages? If yes, and if you switched to new Outlook app, you need to import the On My Computer folders.