A NZ school will indeed admit a new pupil in the middle of the school year. What standard or class he has completed in his own country will be partly irrelevant, because the school systems aren't a match from one country to another - although many of the same topics will be studied in different countries, they may be taken in a totally different order, so the incoming child may have already done parts of a subject that are new to their NZ classmates, and vice versa. Therefore, NZ schools are very used to migrant children needing some help to fit in. What often happens is that they'll test them to see what they know, and fit them into a class depending on that,
as well as their chronological age.