Do I have to leave NZ to apply for a Work Visa?

Unless you hold an interim Visa, then no you can change your Visa type whilst you are in the country. Interim Visas holders are generally not allowed to apply for a further temporary Visa so you would have to leave NZ in order to reapply. However if you are here on a valid, Visitor or Student Visa and want to change to a Work Visa, you can do so.