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Speaking on the eve of the royal visit by the Duke and Duchess of Cambridge, the former deputy prime minister said the country has been moving towards republicanism "for a long time".
"I'm quite certain the royal family understands that completely," Sir Don said.
"[There are] 54 countries in the Commonwealth, only 16 are realms, and I can tell you now that one Caribbean publicly, and three Caribbean, privately are probably going to give up that relationship with the monarchy when the Queen dies. So it is a diminishing group of countries, and the important thing is for us to openly and candidly debate the issue."
Sir Don, who sat as the secretary-general of the Commonwealth of Nations for eight years, said he believed New Zealand would eventually become a republic.
"I think it's inevitable," he told TV One's Q+A programme this morning.
"I don't know when, and I'm not going to campaign actively one way or the other. I have a great respect for Her Majesty and I have respect for [Prince] Charles, but it's a debate that will continue and it's important we have a good debate about this and about the flag."
Prince William and Catherine are due to arrive in Wellington tomorrow with their baby Prince George, on his first royal tour since his birth last July.
They will carry out a number of engagements across the country before flying to Australia to continue the tour.
Sir Don said he believed Kiwis will come out to see the royal couple.
"There's the celebrity side of it, these are two very attractive young people, and wherever they go, in the United States or elsewhere, they get crowds, so yes I believe people will come out," he said.