Generally speaking, these updates tend to be free. This has been true for things like my VPN client, Citrix Receiver and others. In rare cases I have had to go to the vendor’s Web site and download a completely new version of the app so that it would function with High Sierra. I recommend that you check for updates for any of your installed applications just to make sure they are fully patched for the new Apple operating system. Once complete, you should then be able to use Outlook without issue.
This will run an application that will take you through the update process.
To do this, click on the Help menu and select Check for Updates. All you have to do is open any of the other Office applications such as Excel or Word and run the update.