The inquiry in the conviction of David Harold Eastman remains stalled, with a challenge to his legal representatives still unresolved.

Eastman is serving a life sentence for the 1989 shooting murder of Australian Federal Police assistant commissioner Colin Winchester.

An inquiry into his conviction has been delayed because Eastman been unable to lock in a legal team.

The ACT Bar Association has advised his legal team they each had a conflict of interest and should withdraw.

In a hearing today it was revealed that two of the lawyers, Alyn Doig and Terry O'Donnell who is likely to be called as a witness have returned their briefs.

But senior barrister John Harris has asked the association to reconsider.

Inquiry head Acting Justice Kevin Duggan says the court hearing can not continue until Eastman's representation is in place.

For the first time Eastman joined the hearing via video link from the Canberra jail.