The Verdict: Need More Info
You can apply for residence once you have held the work visa for 24 months and stayed active in your declared field throughout. Work out your 24-month date now and keep a running file of evidence until then.
Active engagement is shown by earnings from the field, performance or competition schedules, and letters from your sponsoring organisation. Time spent mainly teaching, or a season lost to injury, can leave the record thin; ask your sponsor early for their letter.
You will also need health checks including a chest X-ray, and police certificates under six months old if you are 17 or over.
The resident visa's travel conditions expire after two years, so apply for a permanent resident visa before travelling after that. Citizenship needs five years holding residence, 1,350 days in New Zealand and at least 240 in each year.