McSkimming resigned as the country's second most powerful policeman last month amid a four-month investigation by the Independent Police Conduct Authority and police.
His resignation came after Police Minister Mark Mitchell said he was recently informed of allegations of a "very serious nature", separate to the investigation that led to him being suspended.
RNZ earlier revealed that pornography found on McSkimming's work computer is being investigated as alleged objectionable material. He declined to comment on the allegations through his lawyer.
His lawyer Linda Clark was earlier granted a rare "superinjunction" by Justice Grau that prohibited reporting that disclosed the nature of the allegedly objectionable material, as well as the existence of the injunction itself.
A teleconference was then held by Justice Gwyn from the High Court at Wellington to discuss the injunction with Clark, police and legal counsel for RNZ, Stuff and NZME.
Following that conference, the order prohibiting publication of the nature of the allegedly objectionable material was continued - but the order prohibiting the existence of the injunction was not continued, meaning RNZ could report the fact of McSkimming's application and the interim result.
A hearing will be held in the High Court at Wellington today in relation to the injunction.
RNZ, NZME and Stuff will be jointly represented by Robert Stewart, KC.
The IPCA earlier announced it was investigating allegations of misconduct by McSkimming following a complaint from a member of the public.
It is also investigating if there was misconduct or neglect of duty by any other police officers or employee in responding to the allegations.
Police Commissioner Richard Chambers said in an earlier statement that he appreciated that the resignation of McSkimming raised questions, but the criminal investigation couldn't be "compromised by commenting on the circumstances of it at this point".
"However, I can say that I have always made it very clear that trust and confidence in police is a top priority for me as commissioner," Chambers said.
"I take very seriously anything that puts trust and confidence and the reputation of police at risk and will act to address it."
McSkimming's resignation came after Mitchell said he was recently informed of allegations of a "very serious nature", separate to the probe that led to him being suspended.
Mitchell said McSkimming resigned before he could be dismissed. He did not say what the allegations were.
However, the minister said the Policing Act was "very clear".
"A deputy commissioner of police must be a 'fit and proper' person. They are rightly held to the highest standards of conduct and this new information called into serious question Mr McSkimming's fitness for office.
"When Mr McSkimming was invited to respond to these allegations he chose to resign. Mr McSkimming's resignation has confirmed my view that his continuation in the role was untenable."
