Down, 24, has played nine ODIs and earlier this year scored a century against the Australia Governor-General's XI. Mair, 20, has so far appeared in three ODIs and three T20Is having made her debut against India in February.
"I want to bowl fast, so my training will be centred around that and working with bowling coach Jacob Oram to get the best out of my action," Mair said. "I'm excited for what's ahead and this contract gives me the resources and time to really commit and focus my energy on cricket."
Meanwhile, Priest has the chance to resume an international career in which she has made 154 appearances across ODIs and T20Is. Her last appearance came during the 2017 World Cup in England with former head coach Haidee Tiffen citing fitness issues for her omission. Earlier this year she enjoyed an impressive KSL campaign in England where she made 365 runs in 11 matches for Western Storm to finish as the fourth-leading run-scorer.
Allrounder Peterson also returns having missed out on last year's central contracts while Kate Ebrahim and Jess Watkin drop off.
The list of contracts is the first major announcement since Bob Carter was named the head coach with his focus now on building a squad for next year's T20 World Cup.
"It's a big few months ahead as we look forward to the South Africa series here in New Zealand, then the ICC T20 World Cup in Australia next year," he said. "Competition within a team is most certainly a positive for the environment. It's natural when you have professional athletes wanting to improve and play for their country."
New Zealand will be without captain Amy Satterthwaite this season following her announcement that she was expecting her first child. A new captain has yet to be confirmed ahead of a home summer that features the visit of South Africa before the T20 World Cup in February and March.
Central contracts Suzie Bates, Bernadine Bezuidenhout, Sophie Devine, Lauren Down, Maddy Green, Holly Huddleston, Hayley Jensen, Leigh Kasperek, Amelia Kerr, Rosemary Mair, Katey Martin, Katie Perkins, Anna Peterson, Rachel Priest, Hannah Rowe, Amy Satterthwaite, Lea Tahuhu