Variable starting and ending dates are not supported. Gibbon uses school-wide terms which are the same for all forms and consequently all courses. I’m afraid, there’s no simple solution for your scenario. However, Gibbon is very flexible and you should still be able to use it with little compromises here and there.
My school has different levels that start at different times. Like Roman has mentioned, there is one set of terms for the whole school, but you can have separate timetables for each year group, and set them to start and end on different days. For teachers and students of different year groups, the school may appear open before their start date, but the timetable is blank until their official start. This setup has worked quite well for us.