Mr Ashby and his solicitor Michael Harmer are seeking leave to appeal the dismissal of the Peter Slipper sexual harassment case on the grounds that the judge erred in his findings.
In a scathing judgment, Justice Rares found Mr Ashby and Mr Harmer had included allegations in the originating claim that Mr Slipper misused cab vouchers "for the purpose of injuring Mr Slipper and for no legitimate forensic purpose".
After the case was dismissed, Mr Slipper applied for Mr Ashby and Harmers Workplace Lawyers to pay all his costs on an indemnity basis.
Mr Harmer appeared in court, where Justice Arthur Emmett was told the parties were seeking to expedite the matter.
Mr Harmer was not a party to the proceedings against the former federal Speaker, but he is seeking leave to appeal on the grounds that the judgment contained "serious adverse findings impacting upon (his) professional reputation and standing".
Justice Emmett set the matter down for a hearing in May, with a date yet to be decided.
"The applications for leave to appeal should be heard before the full court in the May sittings and if (leave to appeal) is granted the appeals will be heard at the same time," Justice Emmett said.
Mr Slipper's costs application should be heard after the appeal matters were dealt with, he added.
That matter has been set down for a directions hearing on May 30.