Can I convert my overseas driver licence to a NZ one?

Yes, at a specialist overseas-conversion driver licensing agent. Requirements depend on which country issued your licence: "exempt" countries need only a practical test if you've held the licence under 2 years; "non-exempt" countries require both a theory and practical test. You must present the physical licence (not just an international driving permit), with an English translation if needed. You can drive on your overseas car licence for up to 18 months after arriving (12 months for motorcycle/truck) — start the conversion well before that runs out. Source: NZ Transport Agency (Waka Kotahi) — Converting an overseas driver licence.