There 60 places @ yr 3, 20 @ yr7 and 20 @ yr9, so you are right spaces are tricky outside these points of entry; some years there are none available in particular yr groups. It is impossible to predict!
For yr 4 there would be a place, if the yr either wasn't filled in yr3 or if someone leaves.
Are you looking for Sept 18 or 19?
If 18, you need to call the school now and see if there are any spaces. The main sitting is January, so any spaces may have been offered already. But the standard of candidates may not have been high enough, and spaces may come up after Easter - pupils have to give term's notice. I know people whose children have got in from the June sitting, so not impossible.
If 19. I would think about bringing entry forward and seeing if you could do a late sitting for yr 3 Sept 18. There could be spaces once offers and the waiting list shake out. The school will keep spaces free if there are no suitable candidates rather than lower standards.
CLFS don't take in yr transfers as far as I know.
The best thing is talk to admissions - they will be very straight with you. Obviously they won't know at this stage whether there would be spaces for 19 entry, but can advise about 18 entry.
Bond books are the best books for prep for the exams.