Lawyers for Bruce Lehrmann applied for the dates to be vacated, citing a lack of available barristers with his previous counsel now unavailable to run the trial that is set to start on Monday.
Lehrmann has been committed to stand trial in the ACT Supreme Court for allegedly raping then Liberal staffer Ms Higgins in an office inside Parliament House in March 2019.
The court heard the reason the previous counsel was no longer available were not the fault of Lehrmann.
It was handed an affidavit designed to explain why no new counsel could be found, but Chief Justice Lucy McCallum said it "tells me very little", adding it implied there were no barristers available Australia-wide.
She said she would need more evidence before vacating the trial dates, with the matter already having been pushed back a number of times.
"I appreciate that it might be a difficult proposition to obtain a barrister ready to start the trial next Monday ... but what you've given me is a blanket 'we can't find anyone, no one's available ever'," she said.
Chief Justice McCallum adjourned the application until Thursday to allow the defence to prepare more evidence regarding vacating the dates.
It was heard the matter could potentially start on June 20 or June 27 if it would enable a new barrister to represent Lehrmann.
The trial is listed to run for four weeks.
Lehrmann has pleaded not guilty.
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