The incoming New Zealand prime minister, Jacinda Ardern, hopes the Turnbull government does not go ahead and restrict New Zealanders from university courses in Australia as she may be forced to end a reciprocal arrangement.

Ardern told Sky News on Sunday she hoped the mutual access continued. “But if we do find New Zealanders aren’t able to access tertiary education the same way as Australians currently do, there will be flow-on effects here,” she said.

She also intends to stick with the 11-member Trans-Pacific Partnership negotiations as long as she can limit foreign investment in New Zealand housing.

“Our view has been that there has to be a balance between delivering for our exporters but also making sure we can protect the ability of New Zealanders to buy homes,” she said.

She insisted her Labour government believed in free trade and would do so in the future. But she said the economy must deliver for all New Zealanders.

“At the moment New Zealanders are not seeing the gains of economic prosperity,” she said. “What is the point, for instance, of having up to 3% growth when you have some of the worst homelessness in the OECD.”