Lawyers for Bruce Lehrmann say they will seek a permanent halt to criminal proceedings and a takedown order for media articles.
Lehrmann is accused of raping former Liberal staffer Brittany Higgins in a federal minister's office in Parliament House and has pleaded not guilty.
Defence barrister David Campbell said Lehrmann would be seeking to permanently stay the proceedings given the publicity of the case prejudicing a fair trial, and failing this, a temporary stay.
Mr Campbell also foreshadowed an application for a takedown order of media articles and an application to prevent any future publication of the issue.
The defence will be writing to media outlets in the next 48 hours seeking consent for a takedown before an official application is made.
Crown prosecutor Shane Drumgold applied for a non-publication order on Higgins' name associated with the stay application, saying her name had become a key search term in the lead-up to the case.
"The concern is the headline will be 'stay application in the Higgins' matter'," he told the court.
"It appears the concern in this matter is the story becomes the story, and then the story of the story becomes the story."
Mr Drumgold said prohibiting the publication of Higgins' name with regard to the stay application will "go some way to ameliorating the harm".
Chief Justice Lucy McCallum questioned how publishing the foreshadowing of a stay application would prejudice the trial, saying she was not convinced of the argument on Wednesday, but could revisit the matter when it next comes before the court.
But Chief Justice McCallum said it did not give the media "free licence" to publish what they want ahead of the case.
"The more this case is ventilated in public forums the more likely it is the accused will not be able to have a fair trial", which would likely result in a temporary or permanent stay, she told the court.
The chief justice also noted that the court had options to suppress evidence and the name of witnesses during the trial to avoid prejudicing the case.
The matter is due to come before the ACT Supreme Court again on April 1.
