If you do a course of the right standard, you will be eligible for a Post-Study Work Visa.
An acceptable qualification for a post-study work visa is New Zealand qualification listed on the New Zealand Qualifications Framework that is either:
a bachelor’s degree (level 7) or higher qualification that involved a single course in New Zealand of 30 weeks or more
a level 4 – 6 qualification that involved a single course in New Zealand of 60 weeks or more
two or more level 4 – 6 qualifications that each involved 30 weeks or more of study in New Zealand, where the level of the last qualification is higher than the first
a National Certificate (Level 4) or New Zealand Certificate (Level 4) relevant to an occupation on Part B or C of our ‘List of Skilled Occupations’ that involved a single course in New Zealand of 60 weeks or more.
English for Speakers of Other Languages (ESOL) qualifications and level 4 qualifications that are not a National Certificate or a New Zealand Certificate aren’t considered acceptable qualifications.
https://www.immigration.govt.nz/new-...ZL&applying=no
See here
https://www.immigration.govt.nz/new-...ZL&applying=no for the details and the evidence required (click down the right hand side of the page) for the open post-study work visa. That one allows you to work for almost any employer, doing anything, for the length of the visa, but it is not renewable, so if you want to stay longer in NZ, you need to use the time to get a skilled job that will make you eligible for one of the temporary work visas (essential skills, or work to residence), and/or Residence under the Skilled Migrant Scheme. (See the INZ website for details of all of those.)
There is also the Employer Assisted version of the Post-Study Work Visa, where an employer has offered you a skilled job as you are coming to the end of your studies.
https://www.immigration.govt.nz/new-...loyer-assisted This one only gives you the right to work for that one employer, until you have got one of the work visas or Residence.