(Don’t empty it.) This effectively trashes your local copy of your Office 365 mail, preferences, rules, signatures, etc. In there open Group Containers > UBF8T346G9.Office > Outlook > Outlook 15 Profiles and move the Again, in the Finder hold the Option key as you choose Go menu > Library. This is a sledgehammer approach, but you might want to try it if nothing else works. In there open Containers and drag the folder to your Trash. In the Finder, hold the Option key as you choose Go menu > Library. Your issue sounds like one resolved by an earlier update. If Outlook still won’t run, verify you’re running the latest version of Office 2016 (currently 15.12.3). If you’re able to get activated, test Outlook. See if you’re able to activate with one of them.
If Outlook won’t launch for you then one of these others should. First, verify your Office 2016 is activated using another application such as Excel, PowerPoint or Word.