The inquiry is currently looking at Eastman's conviction for the 1989 fatal shooting of ACT police chief Colin Winchester, as he sat in his car outside his neighbour's house.

It was ordered by Justice Shayne Marshall last year, after fresh doubt was raised about Eastman's 1995 conviction.

A huge amount of work has already been devoted to the inquiry, and it began hearing evidence last week, including information suggesting Eastman's judge Justice Ken Carruthers had been in possession of a number of psychiatric reports on the accused before the trial.

But the Director of Public Prosecutions last week began action in the ACT Supreme Court, which has the potential to stop the inquiry in its tracks.

The DPP has challenged the legality of the order to conduct the inquiry - made by Justice Marshall in August last year - as well as a decision by Acting Justice Brian Martin earlier this month not to limit its scope.

The application for judicial review of those two decisions came before Chief Justice Helen Murrell on Tuesday morning.

The DPP asked that their challenge be heard as quickly as possible, and that it come before the full bench of the ACT Supreme Court.

Both requests were supported by Eastman's lawyers and by representatives for the Attorney-General Simon Corbell, who is considering whether to intervene.

But Eastman's lawyer told the court there was a "certain irony" in the fact the DPP were pushing for their challenge to be heard as quickly as possible, given one of the decisions they were challenging was made by Justice Marshall over a year ago.

"It is from our perspective strange that the [DPP] has waited until last Friday to place these orders," he said.

But he said it was important the DPP's challenge was resolved as soon as possible, "having dragged its feet now for 15 months".

The DPP's challenge to the decision by Justice Marshall to conduct the inquiry is well outside the time allowed.

That means the DPP will need to apply for an extension of time and show special circumstances that explain the delay.

Their request for an extension will be resolved at the time of the hearing.

Chief Justice Murrell ordered that the challenge be referred to the full bench, and expedited the hearing to take place over three days from December 9.

The court heard it would be technical and complex in nature, and that a lot of the history of the Eastman case would need to be covered.

It also heard there may be problems finding judges to form a full bench of the ACT Supreme Court, due to conflicts of interest.

The DPP raised concerns about any involvement of Justice John Burns and Justice Richard Refshauge, who have both had involvement with the Eastman case in the past.

Justice Hilary Penfold was raised as a possible candidate, but the court was told she may have excused herself from a prior matter relating to Eastman.