Teina Pora was twice wrongly convicted for the crime and spent 22 years in prison before the Privy Council quashed his conviction in 2015. He has since received an apology from the Government and $3.5 million in compensation.
Pora may be called as a witness at Rewa's trial, the hearing was told.
Chambers said a dramatised 90-minute television film about Pora's case, In Dark Places, played on TVNZ 1 last month, was prejudicial to Rewa's case.
The lawyer said public perception compared Pora to Rewa, who maintains he is not the murderer.
In Dark Places was seen by more than 240,000, according to South Pacific Pictures.
The film, Chambers told the court, shows an actor playing Rewa hiding in a closet before Burdett's murder. A similar rape is later foreshadowed in the movie.
"With the release of the film, Mr Rewa cannot get a fair trial," Chambers said.
However, Crown prosecutor Gareth Kayes said: "Publicity alone is certainly not going to win the day for [Rewa]".
The film, Kayes said, carried an artistic licence and focused on Pora rather than Rewa.
The film was due to be removed from TVNZ's online platform six months before the trial.
A stay of proceedings for a murder prosecution against Rewa had previously been applied by the Solicitor-General in 1998.
But last year the Deputy Solicitor-General, Brendan Horsley, on behalf of the Attorney-General, reversed the 1998 stay.
In May, Justice Venning also declined an application by Chambers for a judicial review of the decision to lift the stay.
"The reversal-of-stay document sets out the grounds for the decision, namely that given the quashing of Mr Pora's convictions no one has been held accountable for a murder, and the evidential sufficiency supporting the murder charge against Mr Rewa," he said in his decision.
"There is no evidence before the court of any bad faith on the part of the Attorney-General in relation to the decision to lift the stay. The fact the effect of lifting the stay is that Mr Rewa will face a third trial is not, of itself, sufficient to provide justification for the court to review the Attorney-General's decision. Third trials, although rare, have been held in certain cases."
A stay had never before been lifted in New Zealand's legal history.
In May, Rewa was denied parole, his first hearing before the Parole Board.