Hey Andrei. For the broader events list, past events are automatically kicked onto a “Past Events” page. It can still be accessed on the frontend but isn’t what your readers see by default when they visit the calendar. Are you saying you want to remove the “Past Events” link entirely?
The widget should be pushing past events out by default; once an event has finished, it will be removed from the widget. What are you seeing different? Got a link I can check out to see these issues in action? I’ll try to diagnose best I can from there.