Sept 22 (Reuters) - Rupert Murdoch's departure as the chairman of Fox Corp and News Corp could provide an opportunity to mend the relationship between former President Donald Trump and Fox News as the 2024 election campaign heats up, said a former adviser to Trump and Republican strategists.

A mutually beneficial relationship between Trump and Fox News broke down after the 2020 election in the wake of the network's coverage of the election and the Jan. 6, 2021 Capitol Hill riot by Trump supporters that left five dead and injured more than 140 police officers.

Fox chose in April to settle a defamation lawsuit with Dominion Voting Systems for $787.5 million over its amplification of Trump's false vote-rigging claims in the 2020 election, which legal experts said was the largest settlement ever struck by an American media company.

Rupert Murdoch's son, Lachlan Murdoch, will become the sole chairman of News Corp and continue as the chair and CEO of Fox, the companies said on Thursday, raising questions about how Fox's political coverage may change ahead of the 2024 Republican primaries and presidential election.

Fox News continues to be the number one U.S. cable news network, playing an influential role in U.S. politics. Republicans prize its conservative-leaning audience, but critics accuse it of bias and say it has made U.S. politics more toxic.

Trump is far and away the front-runner for the Republican nomination. If he is selected as the Republican nominee, he would face Biden in a November 2024 general election.

"This provides an opportunity for a reset between President Trump and the Fox News network," Republican strategist Ron Bonjean said of Lachlan Murdoch's appointment. "The question is: does Lachlan Murdoch want to have a positive relationship with former President Donald Trump? Or does he want to see how things play out?"

Fox News did not immediately respond to a request for comment about political coverage under Lachlan Murdoch. Trump does still appear occasionally on Fox News, and gave an interview to the network's chief political anchor, Bret Baier, in June.

An aide to Donald Trump said any response to Rupert Murdoch stepping down would come from Trump himself on his Truth Social media platform. Trump had not made any comment by Thursday evening.

Jason Osborne, an adviser to the former Republican president's 2016 campaign, said he hoped Lachlan Murdoch and other Fox executives would seek to boost Trump coverage and that both sides could mend ties.

"The only path up is regaining those viewers that they lost. And the viewers that they lost veer more towards Trump," Osborne said. "I think there will be outreach if it hasn't already occurred."

Fox executives in 2021 decided to more forcefully rebut Trump's false claims that the 2020 presidential election was stolen from him through voter fraud, a conspiracy theory that fueled the Capitol Hill riot. Fox lost Trump-supporting viewers to smaller, right-wing cable networks such as Newsmax and One America News Network after the decision.

NOT 2016 AGAIN

Fox was a cheerleader for Trump in his ultimately successful 2016 White House campaign against Democrat Hillary Clinton, a symbiotic relationship that continued up to the 2020 election.

Trump boosted Fox's ratings, while Fox boosted Trump politically, said Larry Stuelpnagel, an associate professor of journalism and political science at Northwestern University and a former broadcast journalist.

Dan Cassino, a politics professor at Fairleigh Dickinson University in New Jersey, said he does not believe Fox's coverage of Trump will return to 2016 levels. But he added indications are that Lachlan Murdoch is not anti-Trump and as Trump remains the front-runner, coverage of him will likely be "high volume".

During the Dominion litigation, documents emerged in which Lachlan Murdoch instructed Fox News executives to rein in critical coverage of Trump after he lost the 2020 election.

Analysts said those could be heat-of-the-moment instructions over ratings, rather than a vision for how he wanted to cover Trump in the future.

Karen Finney, a Democratic strategist, said Fox's support of Trump's election lies had been costly, but she was skeptical the network would fundamentally change when it comes to Trump. "Their coverage continues to peddle in misinformation and conspiracy theories," Finney said.

Stuelpnagel said he believed the high cost of the Dominion lawsuit might make Lachlan Murdoch tread carefully on Trump coverage.

"The Dominion lawsuit cost them dearly," Stuelpnagel said. "I think Lachlan is going to be more cautious in how he deals with Trump. I don't see a wholesale change in the direction of network." (Reporting by Tim Reid, Nathan Layne and Alexandra Ulmer; Editing by Heather Timmons and Jamie Freed)