If we want a different school for class 6 next year, when do applications really start?

Our son moves up to class 5 in June. His current school has been fine for the primary years, but we have doubts about the middle years there, mainly section sizes and how computers are taught. I'd rather not be the parent who discovers in January that forms closed in October. For class 6 entry in June 2027, when do schools around Jubilee Hills and Banjara Hills usually open applications? Is it the same cycle as nursery admissions, or later? And do most hold an entrance test for class 6, or an interaction? I'd be grateful to hear what happened in practice rather than what the websites say.