The inquiry into Eastman's conviction for the 1989 murder of Canberra's top cop was scheduled to begin on Monday.

But the start date has been postponed indefinitely after three members of Eastman's legal team were last month forced to stand down due to conflicts of interest.

The court on Monday heard the trio were fighting objections from the Director of Public Prosecutions, partly over their past associations with the case.

Legal Aid solicitor Helen Hayunga told the inquiry that no formal ruling had been made by the ACT Bar Association to exclude the men and the three barristers had not returned their briefs.

Ms Hayunga said Eastman construed the representation issue as interference in his right to select counsel of his choice.

Inquiry judge, Justice Kevin Duggan, scheduled a further directions hearing for later this month to report on the search for Eastman's counsel.

Justice Duggan said if the issue was still unresolved on March 19, he would set a deadline.

He warned if the impasse remained by the cutoff date, he would make a decision himself.

“If it comes to that,” the retired South Australian judge said.

“These issues have to be a resolved as soon as possible, [it's] holding up the inquiry.”

But Counsel assisting, Liesl Chapman SC, assured Justice Duggan, that while the inquiry had stalled in the court room, her office was working full-time behind the scenes.

Ms Chapman told the court her office had begun contacting witnesses and taking statements.

The barrister also outlined which subpoenas had been returned.