The application cites the Supreme Court's recent "Haronga" decision, in which the court ordered the tribunal to make a decision on returning state forestry land near Gisborne.
So rarely is the power used - only once has the tribunal ordered land returned - that some have likened it to a "kehua" or ghost.
Ngati Kahu originally asked the court to look at the issue in 2007, but it was put on hold so the Crown and iwi could negotiate an outcome.
In filed tribunal documents, lawyers for the tribe said those negotiations proved fruitless and there was a pressing need for the tribunal to act. Those efforts included writing its own deal - which the Crown has rejected.
"We submit the Crown is seeking to conclude, prior to the general election, deeds of settlement with other ... iwi [Te Aupouri, Te Rarawa, Ngai Takoto and Ngati Kuri] over land in which Ngati Kahu has claims and interests. "Counsel submit that if those settlements are concluded, Ngati Kahu will be severely prejudiced."
The four other tribes are members of the Te Hiku Forum which is negotiating with the Crown over settlement. Professor Mutu said Ngati Kahu was a part of the forum but other iwi "booted it out", a claim Treaty Negotiations Minister Christopher Finlayson denies.
Professor Mutu gave an assurance to other iwi that her tribe wasn't asking for anything that wasn't fair.
Forum chairman Haami Piripi said he supported Ngati Kahu needing to do what they felt was right for them.
But he believed the runanga was on a "hiding to nothing", as the Haronga decision applied to land which originally belonged to a Maori incorporation.
Ngati Kahu's runanga had never owned forestry land.