Work DURING study in New Zealand:
You can work up to 20 hrs per week during study period and full-time (generally 40 hrs per week) during vacations. You can earn about $12 per hour. Students generally find their own part time jobs. Sometimes these are even advertised by the Institution
The visa in your passport should state if and when you may work. You may also have a letter from Immigration New Zealand stating that your visa allows you to work.
Work AFTER study in New Zealand (Post study work visa in New Zealand):
After successful course completion, you will automatically get a 12 months ‘Work Permit’ (in most cases, this will be done at your Institution). This is your job search visa in New Zealand that allows you to find opportunities to work in NZ. You can work full-time in any job of your choice. But remember, if you are aiming a NZ Permanent Residency, then you have to find a job relevant to your course (that you have finished studying in New Zealand).
Immigration New Zealand: Once you have finished your study in New Zealand, you may be able to work in New Zealand for up to four years, and after that, apply to work or live in NZ longer term. Your chances of getting further work are higher if you have the skills that New Zealand urgently needs. Here’s the skill shortage list check.
The study to work pathway has the following two steps:
Post-study work visa (open):
This visa gives you up to 12 months to identify jobs in New Zealand and get a job in a field related to your studies. During the period that you are finding relevant jobs in New Zealand, you are allowed to work in any job to support yourself
Post-study work visa (employer assisted):
This visa lets you stay in New Zealand to gain work experience for a further two years (or three years if work experience is required as part of a professional registration). This visa relates to a specific job with a specific employer
More information about Study to Work in New Zealand is available here (New Zealand Immigration)
After your post-study work visa (employer assisted) you may qualify for a New Zealand resident visa under the Skilled Migrant Category. If your work is in an occupation that has skill shortages, this improves your chances of being allowed to stay, either with work visas or residence.
All we can say is permanent residency (PR) in New Zealand is way easier as compared to most other countries