The parents of 20-year-old Mr Leveson have waited 3453 days to bring their boy home. In November, they were left devastated when a search of the Royal National Park failed to find him and now they face a further delay in finding out what happened to their son.

During a brief mention in the NSW Coroner's Court on Monday, the inquest into Mr Leveson's disappearance was adjourned for a further five months.

However police have stressed that detectives on Mr Leveson's case will use that time to continue searching for the young man's remains.

Mr Leveson was last seen leaving ARQ Nightclub in Darlinghurst in September 2007.

His former boyfriend, Michael Atkins, 54, gave evidence before the inquest was adjourned following sensational developments last November.

In his evidence, he denied any involvement in Mr Leveson's suspected death but later led police to the Royal National Park where he claimed Mr Leveson's body was buried.

Despite searching for days in two different locations in the area south of Sydney, police came away empty handed and Mr Leveson's determined and unwavering parents were devastated.

It was initially expected that Mr Atkins, who now lives in Queensland, would return to the witness box once the inquest resumed this week.

However, Patrick Saidi, barrister for the NSW Police Commissioner, flagged the possibility that Mr Atkins may not come back.

He said one of the issues expected to arise was whether Mr Atkins "with the threat of perjury hanging over his head" was entitled to fall back on the principle of "self-incrimination".

Last year, Deputy State Coroner Elaine Truscott took the unusual step of issuing Mr Atkins with a certificate, granted under section 61 of the Coroner's Act, under which he would not be prosecuted for evidence he gave during the inquest.

In a bid to find Mr Leveson's body, his parents Mark and Faye consented with the Attorney-General in offering Mr Atkins a second olive branch.

Mr Atkins agreed to a deal under which he would be granted immunity from a perjury charge if he showed investigators where Mr Leveson's body was.

The fact that Mr Atkins then pointed police to the Royal National Park as the burial site for Mr Leveson contradicted his earlier evidence in the inquest.

Mr Atkins was charged with Mr Leveson's murder and manslaughter but found not guilty by a jury in 2009.

It is unclear at this stage whether he will be required to get back in the witness box and whether the section 61 certificate would afford him further protection by way of immunity.

The court heard on Monday there were serious legal issues and complexities at play.

Mr Saidi sought to reassure Mr Leveson's family that the lengthy inquest adjournment would not have an impact on the police's resolve to find his body.

"They can be reassured, if it is put over to August, that the detectives in charge will have that further time to ... continue to go down the avenue of trying to achieve what we all want to achieve," he said.

Mark Leveson's response was a testament to his family's patience over almost 10 years, he said.

"Matt was last seen 3453 days ago," he told the court.

"This inquest began 407 days ago."

Outside court, Faye Leveson added: "We are going to bring him home."

The inquest will resume in August.