As per the INZ website, the following are deemed 'Essential Health Workers' during the Covid-19 lockdown:

Medical Doctors
Nurses
Midwives
Psychologists
Physiotherapists
Technical and support staff working in:
Theatre
Laboratory
Radiology
Cardiology Blood service
Nuclear medicine
Oncology
Haematology
Pathology
Hyperbaric medicine
Mortuary
Research Staff
Support staff working in:
Aged care
Palliative/hospice care
Mental health
Child health
Forensic care

If you are employed in one of these occupations and either have a work visa application lodged with INZ now or are planning to lodge one very soon, you can request that your application be processed urgently by sending a request to EmploymentVisaEscalations@mbie.govt.nz.

I have been advised that those who are based offshore and are in one of the above occupations can also send a request to this email address regarding the process of being granted an exception to come onshore given the current border restrictions.