She confirmed this afternoon she had filed papers with the Court of Appeal and there would likely be a hearing before her client's next High Court appearance.
It would be several days before the court scheduled the exact date and suppression will continue until then.
The continued secrecy will add further frustration to the Morris family, who stormed out of court yesterday led by the victim's father Chris.
"He should've thought about name suppression before he killed my son. F***ing egg," he said.
Mr Morris, 26, suffered a fatal head injury during a confrontation outside a party in the West Auckland suburb of Massey just over a month ago.
He was held by Ms Elder-Holmes, his partner of six years, as he lay dying.
A four-week trial has been scheduled for August next year.