A man acquitted seven years ago for the murder of his then-boyfriend has led police to his possible grave site in rugged bushland south of Sydney after being granted immunity from prosecution.

In a sensational development in a long-running case, the inquest into Matthew Leveson's disappearance nine years ago was adjourned on Thursday.

Police are now searching a location in the Royal National Park, not far from where Mr Leveson lived before he disappeared in 2007, for the 20-year-old man's body.

Officers have been led there by his former partner, Michael Atkins, who was found not guilty of the murder and manslaughter of Mr Leveson following a trial in 2009.