How much study gap is acceptable in New Zealand? I got my Master about 4 years ago from Iran. Since then, I have been working in a research group and published 4 papers in journals with IF between 1.767 to 4.594, including a paper related to my dissertation, and still working on 2 other research projects with my former supervisor in the university in Iran, based in Tehran. I was about to apply for pursuing my Ph.D. in New Zealand in the fields of Mathematics and Industrial Engineering when the pandemic emerged. I am a bit worried that the educational gap affects my plan negatively. Plus, I am at the age of 44 with 18 years of practical experience in industries and research, and I cannot fall asleep because of my worrieness.
It sounds like you have still being doing research and publishing since your masters. If you have still been keeping your skills fresh, that means you haven't really had a gap, regardless of whether or not you were registered as a student. Just explain this when applying and your gap will not be a concern. Your recommendation letters and publications can attest to that fact.
Age should not be a concern from the university's perspective. Although, a prospective supervisor may wonder about your perspective -- why do you want to do a PhD now? why not earlier? If you can give a good answer about your aspirations, then that will allay any concerns.