Priest, 32, who has played 86 one day internationals has been left out of the 14 strong squad named today for three one dayers and four Twenty20 matches against Pakistan in the United Arab Emirates later this month.
Spinner Erin Birmingham has also been left out of the side because of fitness concerns.
Coach Haidee Tiffen said Priest needed to improve her physical conditioning in order to perform consistently at the international level.
"We've been clear with Rachel about the areas we want to see her improve in. She's taken the feedback on board and is committed to putting the work in.
"We believe Rachel still has a lot to offer the White Ferns," she said.
Tiffen said the tour presented a good chance to build some depth at wicket-keeper.
Priest's place in the side has been taken by Otago's Katey Martin.
"It's a position we're aware needs work and so it's great to be able to give Katey this opportunity," said Tiffen.
"She obviously does the job for the Otago Sparks and has kept wickets for us in the past, but we're keen to see her behind the stumps for a full tour across different formats."
Tiffen said the side was looking to put the disappointment of July's World Cup campaign, where they failed to make the top four for the first time, behind them.
"We can't wait to get back out on the park and play some cricket," she said.
"This is the start of some important games for the White Ferns as we look to prepare for next year's ICC World T20 in the Caribbean.
The One Day series also signals the start of the ICC Women's Championship and qualifying for the Women's Cricket World Cup 2021, which is being hosted in New Zealand.
New Zealand squad:
Suzie Bates (c), Sam Curtis, Sophie Devine, Maddy Green, Holly Huddleston, Leigh Kasperek, Amelia Kerr, Katey Martin, Thamsyn Newton, Katie Perkins,
Anna Peterson, Hannah Rowe, Amy Satterthwaite, Lea Tahuhu.