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?
Do you have any send and receive error messages? That would help identifying the problem.
Did you try removing the account from Outlook and adding it back? If asked to remove it from all devices, say yes. This removes the cached content from the Microsoft cloud servers, which is a frequent cause of sync issues.