The scheduled date, March 4, was switched to a directions hearing after three members of Eastman's legal team had to stand down due to conflicts of interests.

But preparations for the inquiry continued unabated when the gun that could explain flecks of gunshot residue found in the boot of Eastman's car underwent test firing in Canberra this week.

Further forensic analysis of the rifle is scheduled to start at an Adelaide laboratory next week.

In 1995, a jury found Eastman guilty of assistant police commissioner Colin Winchester's murder, and he was subsequently sentenced to life behind bars.

Eastman has served 17 years of the sentence but has always maintained his innocence, fighting the verdict all the way to the High Court. The inquiry was called after the emergence of a witness who claims he borrowed Eastman's car to go rabbit-shooting and put his .22 rifle in the boot.

The evidence could explain why gunshot residue was found in Eastman's car.

But the loss of three members of Eastman's legal team has threatened to delay the inquiry.

Acting Justice Kevin Duggan told the court that the inquiry must start as soon as possible.

Justice Duggan urged Legal Aid solicitor Helen Hayunga to find counsel to act for Eastman quickly.

''It goes without saying that we cannot commence the inquiry proper unless we have appropriate counsel for Mr Eastman,'' the judge said.