If you don't want your past events to be displayed on search result of Joomla core Smart Search, you can use Events Booking - Delete Past Events Index scheduled task. Each time the task is executed, it will find and delete index of events which are older than 24 hours compare to the current date time, thus prevent these past events are being searchable via smart search

This scheduled task should not be run so often. Run it every 12 or 24 hours should be enough. So you can setup Basic Fields to following values