Prime Minister Jacinda Ardern is hosting her first post-Cabinet press conference after returning to Parliament.

Ardern is expected to make a trade-related announcement, likely to be the new Trade Commission Labour has proposed to advise the Government on trade agreements.

That is set to include representatives from business, the unions and academia, as well as Māori.

Ardern is also likely to face questions on business confidence and the appointment of Police deputy commissioner Wally Haumaha.

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That appointment was signed off by Ardern but has since been called into question because of support he voiced for Brad Shipton and Bob Schollum during an investigation into historic rape allegations by Louise Nicholas. They were found not guilty of that but both had served time for another rape.

Internal Affairs Minister Tracey Martin, a NZ First MP, has been charged with the inquiry into that appointment. Further links between Haumaha, who once sought selection for NZ First, and the party's MPs have been revealed today.

National Party MP Chris Bishop has called for the inquiry to be removed from Martin.

The first inquiry head Pauline Kingi withdrew last week after publicity about her endorsements of Haumaha on LinkedIn and involvement on the advisory board for the Counties-Manukau Police district.