Welcome to Android Central! Do you know if you entered those calendar events into the calendar for the Phone account, Samsung account, or Google account? Google Calendar events are the easiest to deal with, because they sync automatically with your Google Calendar in the cloud -- so once you log into the new phone with the same Google account, they sync automatically with your calendar.
Just to be sure, this is the old Galaxy S4 phone, and not the newer Galaxy Tab S4, right?