Jurors heard yesterday that the former Sun and News of the World (NotW) editor also allegedly authorised journalists to pay a member of the armed forces for a picture of Prince William wearing a bikini.
Prosecutor Andrew Edis, QC, outlined the details as part of the charges Mrs Brooks is facing for allegedly conspiring to commit misconduct in a public office.
Mrs Brooks denies the charges, as well as allegations of phone hacking.
Mr Edis said that in 2006 while editor of The Sun, Mrs Brooks authorised payments to an official who gave details about dead soldiers out before they were officially announced by the MoD.
"It may concern, for example, the death of active servicemen," he said. "It really matters when it is released and how it was released to other people affected by it."
The court was told about emails to Mrs Brooks asking for authorisation for various cash payments, all said to have been approved by her.
"These are emails which reveal what Mrs Brooks knew when she authorised the payments, and the fact that she did authorise the payments, and we know from the timeline what the payments refer to and the fact that they were made.
"The prosecution suggest that in behaving in that way Mrs Brooks was involved in a conspiracy to commit the criminal offence of misconduct in a public office and that she knew it."
The court heard Mrs Brooks also authorised a Sun journalist to pay a member of the armed forces for a picture of William dressed in a bikini.
In June 2006, she was asked to authorise a cash payment of £4000 for the picture of the royal, who was at a party dressed as a Bond girl, the court was told.
Mr Edis said an email from the journalist was forwarded to Mrs Brooks that said: "My best contact at Sandhurst who has provided some great stuff over a period of months is offering us a picture of William at a James Bond party dressed as a Bond girl. He is wearing a bikini and an open Hawaiian shirt."
Mr Edis said that another story came from a voicemail illegally accessed by private investigator Glenn Mulcaire for former royal editor Clive Goodman.
Jurors heard the story had come from a voicemail message left by Prince Harry for his private secretary Jamie Lowther-Pinkerton, a former member of the armed forces.
The court heard the prince asked his aide if he "had any information at all" about the Iranian embassy siege - the scene of a British special forces operation in 1980 - adding: "Because I need to write an essay quite quickly on that but I need some extra info. Please, please email it to me or text me."
The tabloid also obtained information about Prince William being "shot" during a training exercise in Aldershot, jurors were told.
Mr Edis said: "William found himself in the wrong place during a night exercise so he got shot, pretend shot.
"There is a voicemail, recording of a voicemail, in which Prince William says something about that. So it's a phone hack."
The NotW journalists also targeted Prince Charles's private secretary Sir Michael Peat over false rumours the aide had been having an affair, it is alleged.
Prosecutors claim Goodman paid for two copies of a Royal telephone directory from palace police officers, with the funds allegedly authorised by Andy Coulson, the Prime Minister's former spin doctor, who is also on trial accused of conspiracy to hack phones and conspiring with others to commit misconduct in public office.
Fifteen copies were found in his home when it was searched in 2006, and of those it is claimed another two belonged to police but were not necessarily sold by officers, the court heard.
One had an officer's fingerprint on it while another bore an officer's handwriting.
It is claimed Mr Coulson also ordered that the phone of Calum Best, the son of former footballer George Best, be hacked.
Mrs Brooks, 45, of Oxfordshire; Mr Coulson, also 45, from Kent; Mr Edmondson, 44, of London; and the tabloid's ex-managing editor Stuart Kuttner, 73, from Essex, all deny conspiring with others to hack phones between October 3, 2000 and August 9, 2006.
Mrs Brooks is also accused of two counts of conspiring with others to commit misconduct in public office linked to alleged inappropriate payments to public officials.
Mr Coulson is also facing two allegations that he conspired with Goodman, 56, from Surrey, and others to commit misconduct in public office.
Mrs Brooks also faces two allegations of conspiracy to pervert the course of justice with others, including her husband, race horse trainer Charlie Brooks.
The case was adjourned until Monday.