How do I force my calendar application to refresh a calendar subscription?

When you update a calendar subscription, this change is not reflected immediately in your calendar. You can just wait from one day or, in worst cases, one week.

In macOS Outlook there is a command to refresh a calendar. However, it only fetches new data from the Outlook server, not from the source site. So in practise in most cases it does nothing that would affect the content. The best option is just to wait for Outlook to refresh the data.

The other option is to remove the calendar subscription and add it back to Outlook. This is done at Web Outlook.