State-Owned Enterprises Minister Tony Ryall told TVNZ at the weekend he could not rule out a sale this year.
"Ministers are going to consider the Air New Zealand shareholding in the next few weeks and then we'll take advice and make a decision on that."
Palmer said he had committed to the board last year that he would see through the transition to a new chief executive.
"Now that Christopher Luxon and his management team are off to a flying start delivering our Go Beyond plan I am confident I will leave the business in tremendous shape," Palmer said.
Carter said he felt privileged to become Air New Zealand's chairman and paid tribute to Palmer.
"John took over as chairman in 2001 during one of the darkest periods in the airline and corporate New Zealand's history. Over the course of more than a decade John has ensured the board supported successive management teams under three outstanding chief executive officers to see the airline return to its place as one of the best in the world."
A Morningstar note out late last week said Air New Zealand was the "best of breed". Its cost structure meant it was well positioned to endure pricing pressure from heightened competition and is well positioned to realise growth ambitions over the next decade with new Boeing 787 aircraft.