As standard, a course must be booked prior to its start date. However, you may choose to allow your customers to book onto any remaining course sessions.
To enable this in the date and time section (when editing or creating your course), click Advanced Settings. You can change Booking on the Course to clients can book on the remainder after the start date.
Please note that the price of the course will not change after the start date. If you wish to reduce its price, you will need to manually edit the price of the course after the start date (and after subsequent sessions also occur).