1. Keep your mail sorted into folders
In many cases, Outlook does work properly with folders as large as 10.000 items and more, but decreasing the folder size can improve the performance drastically, and generally this is the first troubleshooting step to be done in a case of slow/freezing Outlook client.
You can move the items using Office 365 client.
Read the following Microsoft Office articles for more information:
2. Keep the number of subfolders in Inbox and Sent Items to minimum
Instead, it is preferable to create new folders on top level. The same level as Inbox and Sent Items are for better performance.
3. Move folders and multiple items in O365
Moving big folders or a lot of items at once in desktop Outlook client takes significant time to synchronize with the server. Moving a lot of items can often cause disruption in the mailbox if the connection fails for a moment, for example, due to high network usage or your computer’s CPU load. On the other hand, changes made in Office 365 occur directly on the server and thus happen instantaneously.
4. Clear affected folder's cache in case of content mismatch
If you see that Outlook 2013/Outlook 2016 for Mac and Outlook Web App folders don't match, you may want to reload the cache to fix the issue.
5. Re-create the Microsoft Office Identity
If the Outlook 2013 client becomes slow and unresponsive, or stops syncing completely, while Outlook Web App and/or other clients work fine, it is most likely an indicator of corrupted Outlook database. In this case, it is recommended to rebuild, or remove, and re-create the Microsoft Office identity or Outlook Profile on Outlook 2016 for Mac. If you do not have any other mailboxes in your Outlook profile, we recommend removing and re-creating the identity.