Administrator of the Government

The Letters Patent provide for an order of succession if the Office of Governor-General is vacant or the Governor-General is incapacitated, outside the country or otherwise unable to perform his or her duties. 

This "acting Governor-General" is known as the Administrator of the Government.  First in line of succession is the Chief Justice followed by the next most senior member of the New Zealand judiciary.  

The Administrator is required to take an oath similar to the Governor-General and may exercise all of the powers of the Governor-General.