You must still hold a valid overseas drivers licence to drive in NZ. A valid licence means it must be current (not expired), and you must not have been disqualified or suspended from driving in the country your licence was issued or in NZ.
If you are in the part way through converting your overseas licence, you can continue to drive using your overseas licence if you:
> passed the theory test on or after 18 December 2020, and
> last entered NZ between 2 January 2019 and 17 December 2020.
You will have a supervisor condition showing on your NZ licence, but you can drive using your overseas licence (without a supervisor) instead. This only applies until you sit the practical driving test to complete your overseas conversion or your overseas licence becomes invalid. If you sit and fail the practical driving test, you can’t use your overseas driver licence anymore and will need to drive with a supervisor at all times.