While May will hear Ardern's reminder that New Zealand is high on the list of countries Britain wants to negotiate free trade agreements with, it likely won't be high on her list of short-term priorities.
Before Britain is in any position to negotiate free trade agreements, the House of Commons must first agree on a way forward or face a so-called "hard Brexit" on March 29 – that is leaving the European Union with no plan.
Options include a new referendum, May softening her "red lines", the key issues she has opposed in negotiations, or possibly seeking an extension to the exit date.
While May has dropped out of attending the World Economic Forum (WEF) this year to deal with the Brexit issue, Ardern will be there, along with Finance Minister Grant Robertson.
Following a morning of talks on the sidelines with other world leaders to push New Zealand's trade agenda, Ardern will meet naturalist and broadcaster Sir David Attenborough on Tuesday afternoon (early Wednesday NZT).
The pair will then be part of a panel discussion chaired by former US vice-president Al Gore.
The discussion, which is being livestreamed on the WEF website, will focus on how leaders can take action to safeguard the planet in the face of climate change, pollution and habitat loss.
Ardern will end her first day in Davos attending the chairman's dinner at the Morosani Schweizerhof hotel as a guest of the WEF's founders Klaus and Hilde Schwab.
Ardern is at Davos for two days before heading to Brussels for meetings with European Council and Commission leaders.