The decision comes after the inquiry stalled amid wrangling over legal representation.

Mr Harris, who worked as counsel assisting on a earlier Eastman inquiry, had previously been advised to withdraw as he had a conflict of interest.

At Tuesday's directions hearing, Mr Harris told the inquiry that the ACT Bar Association had reversed its position and he was free to represent Eastman.

But inquiry judge, Justice Kevin Duggan, said he still held concerns that Mr Harris could contradict submissions he made at the earlier probe.

The judge warned he would continue to scrutinise the situation as the inquiry progressed.

With the representation issue resolved, Justice Duggan set a timeframe to investigate the first four terms of reference - Eastman's fitness to plead at his 1995 trial.

Eastman's legal team is expected to argue the trial judge should have ordered an inquiry into the defendant's mental health in 1995 and therefore the conviction should be nullified.

Justice Duggan's decision on that argument would then guide the first four terms of reference.

Eastman was sentenced to life behind bars for the 1989 murder of Australian Federal Police assistant commissioner Colin Winchester, who was shot dead while sitting in his car in the driveway of a Deakin home.

A jury found Eastman guilty of the assassination in 1995, but he has always protested his innocence.

Justice Shane Marshall ordered the current inquiry in August last year after fresh evidence cast doubt on Eastman's guilt.

The judge ordered the probe based on 19 grounds, including fitness to plead, forensic evidence, and the conduct of the prosecution and investigating police.

Testimony from a witness, who claims he borrowed Eastman's car to go rabbit shooting and put his .22 rifle in the boot, is a central element to be tested by the inquiry.

The newly unearthed information could explain gunshot residue found in the car, a crucial feature of the case which helped lead to the conviction.

The inquiry on Tuesday heard that the rifle had undergone testing by an international forensics expert who had returned to his Northern Ireland base to prepare his findings.

Counsel assisting told the inquiry the report would be lodged shortly.

The inquiry is expected to continue next month.