What happens if there are aren’t open spots in your local schools?

We’ll be making the move to Ireland after this current school year. Though we have some areas identified, obviously housing stock will largely determine where we land. Looking at school websites, we wouldn’t be able to attempt to enroll until May at the earliest, after the official enrollment window seems to close for most schools (particularly Educate Together). So what happens if there are simply no spots in your catchment area? Do you apply further away until you find one? Find a private school? Any advice navigating this much appreciated!