Teaching is no longer a skills shortage profession (when we first applied) and so will be treated as just another applicant in the queue for skilled resident visa depending on the level of points you have and the current quota for the cut-off. You will need to submit a resident visa application along with documents to NZQA for assessment on the level of compatible qualifications to NZ standards as well as register with the Teacher's Council. It's quite a lot of stuff to do and no doubt will occupy a good couple of months as you try to sort this out.
In the meantime, you can apply for teaching positions in NZ, which is usually seasonal around June-July and Nov-Dec for positions. Doing so will give you the opportunity to assess the market currently as well as narrow your choices and preferences on where you want to teach - either in the bigger cities or smaller towns, public or state-integrated or private schools or high or low-decile schools etc.
History isn't always in demand but if you can throw in some experience in social studies, English, maybe a foreign language, or even ICT and current affairs subjects as part of your teaching experience, you may be able to find more job openings than just history alone.
My husband who taught in a private school was mainly a physics teacher and he was prepared to teach maths as well but he was hired to teach middle and upper levels of science (which included both chemistry and biology), a bit of ICT thrown in too.