In a very few instances, the Governor-General may exercise a degree of personal discretion, under what are known as the "reserve powers."
The most important of these is the appointment of a Prime Minister following an election, or accepting the resignation of an incumbent Prime Minister.
By convention, the Governor-General will always appoint as Prime Minister the person who has been identified through the government formation process as the person who will lead the party or group of parties that appears able to command the confidence of the House of Representatives.
The Governor-General expects that there will be clear and public statements that a political agreement has been reached and that a government can be formed that will have the support of the new Parliament. The Governor-General abides by the outcome of the government formation process.
Other reserve powers are to dismiss a Prime Minister, to force a dissolution of Parliament and call new elections, to refuse a Prime Minister's request for an election, and to refuse assent to legislation.
These powers to act without or even against ministerial advice are reserved for the most extreme situations and with the exception of the appointment of a Prime Minister following an election, no New Zealand Governor-General has ever needed to use them.