Dismissal
The Prime Minister may advise the Queen to "recall" the Governor-General, and (so long as the Prime Minister has the confidence of the House of Representatives) the Queen is bound by convention to implement the advice of her Prime Minister. As no New Zealand Governor-General has ever been dismissed on the advice of the Prime Minister, it is unclear how quickly the Queen would act on such advice.
Some constitutional lawyers dispute whether the Queen would implement such advice at all, while others argue that the Queen would delay its implementation. Others argue that the Queen would be obliged to follow the Prime Minister's advice, and further that the Queen would be bound to implement the Prime Minister's advice immediately if so advised.
Critics (usually supporters of a New Zealand republic) describe the ability of the Prime Minister to advise the Queen to recall the Governor-General as a flaw in New Zealand's constitutional make up that gives the Governor-General and the Prime Minister the ability to dismiss one another. They argue that this flaw is exacerbated by the reluctance of the monarch or their representatives to become politically involved. Further, they argue that the flaw means the Governor-General is unable to act as the "constitutional backstop" (a term often used to describe the office), or - as was the case with the 1975 Whitlam dismissal in Australia - to resolve a deadlock the Governor-General may choose to dismiss a government despite it having the confidence of the House of Representatives.
Three New Zealand Governors have been recalled from office - William Hobson (who died before he was officially recalled), Captain Robert FitzRoy and Sir George Grey, all before responsible government was granted in 1853.
Read more about this topic: Governor-General Of New Zealand