Dear Sue Hill2,
Thanks for using Microsoft products and posting in the Community.
I'm sorry to hear that you're experiencing synchronization issues with your Gmail account while using Outlook on your Mac. I'm more than willing to assist you.
May I ask if you are using a personal account or a work account?
Usually, Gmail accounts are IMAP, but in order to synchronize with Gmail, Microsoft has created a new protocol called Microsoft Cloud Sync - if a Gmail account is added as a cloud sync account, it will synchronize emails, calendars, and contacts with the Gmail server. This is the default setting - but if you manually add or turn off cloud sync when adding an account, there will be no calendar in Outlook, or sometimes you may encounter email sync issues.
If you have added a Gmail IMAP account using a new protocol called Microsoft Cloud Sync, you need to know that we have some known issues with email:
Reference: Known issues syncing Google accounts to the Microsoft Cloud - Microsoft Support
Regarding clearing cache so that Outlook can resynchronize affected items. You can refer to: Clear the cache in Outlook for Mac - Microsoft Support
If there is any deviation in my understanding, please forgive me and provide me with more details. I am more than happy to continue to help you.
Best Regards,
Addie.C - MSFT | Microsoft Community Support Specialist