Mountbatten-Windsor was arrested late on Thursday (NZ time) due to suspicions of misconduct during his time working as a British trade envoy representing the late Queen.
Constitutional law expert and University of Otago academic Prof Andrew Geddis said the down side of a monarchy was the risk of the next sovereign being a "bad 'un".
Fortunately, Mountbatten-Windsor was eighth in line to the throne and King Charles III seemed to have "curbed his peculiarities that he showed while Prince of Wales".
"The problem with a royal in charge is, if you get one of the family who's a bad 'un — like Andrew — and they’re in the right birth order, that person will be our head of state whether New Zealand likes it or not."
Luckily for New Zealand, if that did happen, there were many avenues for the country to be rid of a monarch.
If New Zealand wanted to ditch the British Royal Family and become a republic, it would be a rather simple process, he said.
One way would be for Parliament to choose a new head of state through an Act.
"At the moment our Constitution Act 1986 simply says the sovereign is our head of state ... we could change that to say whomsoever happens to be the governor-general at that time takes on that role.
"Our Parliament could just do it by legislating."
There would be more questions and processes down the road, but from a legal perspective, it would be as simple as that.
King Charles' younger brother was arrested during a early morning raid on Wood Farm in Sandringham by British police on the day of his 66th birthday.
Emails released as part of the Epstein files, appeared to show him sharing confidential information.
Whether New Zealand wanted to become a republic in the wake of Mountbatten-Windsor’s arrest was not clear, Prof Geddis said.
It was pretty obvious members of the Royal Family probably knew he was "getting up to trouble", but they likely did not ever know the true extent, he said.
"It's highly unlikely the Queen knew he was [allegedly] trafficking underage girls into the country.
"So, he was allowed to get away with some thing and then he's probably taken that rope that he was given and extended it out even further."
