I passed Part 1 of the Illinois Life licensing examination only, how do I have to wait to retake the examination?

You must wait 3 days to retake the examination.  Since you failed Part 2 (laws), you will only need to take Part 2 again. You have 90 days from the original examination date to pass the part that you failed.  Past 90 days, you must take both Part 1 & Part 2.