If you get near the time when your existing visa will expire and your residence visa seems unlikely to have been processed in time, then yes, you will need to apply for a temporary work visa each - that way, if the temporary visa is not ready in time, INZ can issue you with an interim visa to keep you legally in NZ while processing on them finishes (but they can't do that for a residence visa). This can be done even as late as the day of expiry itself, though most people would find it too nerve-racking to leave it that late.
What visas are you currently on? When do they expire?