It seems there was much ado about "the Mooch" for the new White House chief of staff. But if four-star, retired Marine general John Kelly is to succeed in reining in a turbulent Trump administration as gatekeeper to the president, he'll likely need to do a lot more than orchestrate the ouster of Anthony Scaramucci as he reportedly did Monday.

The former White House communications director, who had taken to calling himself "the Mooch," made himself into a liability worth cutting loose after he went on an R-rated tirade to a New Yorker reporter. Kelly, the newly tapped chief of staff, reportedly requested that U.S. President Donald Trump fire Scaramucci. The former hedge fund manager's tenure lasted 11 days.

Forcing Scaramucci out was a "no-brainer" to Chris Whipple, an expert on presidential chiefs of staff. Even so, he said it only amounts to "a good first step" toward Kelly's purported mission to fix a White House in chaos.

• Scaramucci goes on tirade against White House rivals
• Scaramucci appears to implicate Priebus for 'leak' of financial info

Presidential historians agree that how much power the president is willing to cede to his new chief of staff will determine how functional the White House can be. It might also dictate how long Kelly lasts in this role, which he took over from Reince Priebus, who exited last week after serving a tumultuous 189 days.

"Trump is apparently at least listening to Kelly on Day 1. Now comes the hard stuff," said Whipple, author of The Gatekeepers: How the White House Chiefs of Staff Define Every Presidency.

Here's what some experts say Kelly should do next:

Kelly needs to be a gatekeeper

Critics will be watching carefully whether Kelly fulfills the traditional gatekeeper role, limiting direct communications to the president and managing his schedule.

Kelly's military background comes with a deep respect for chain-of-command management, said presidential historian Mike Purdy.

"So, it's going to be very interesting to see, what does that mean for Ivanka Trump and Jared Kushner?" Purdy said of Trump's daughter and son-in-law, close confidants believed to have previously enjoyed free and direct access to Trump.

Chief White House strategist Steve Bannon also seems to be a powerful force behind the scenes, exercising extraordinary influence on Trump. That access could cease under Kelly's watch if he takes a more traditional approach to the post, Purdy said.

Ivanka Trump and Kushner reportedly said they would follow Kelly's lead. Before Scaramucci was sacked, he had allegedly boasted about his direct line of communication with Trump, circumventing the chief of staff. That may have been at least a partial reason for his dismissal.

He will have to challenge the president

While the president reportedly made New Jersey Governor Chris Christie fetch his McDonald's order and called on former chief of staff Reince Priebus to kill an insect in the Oval Office, those kinds of menial tasks won't fly with Kelly.

Unlike some other staffers, the general isn't expected "to allow president Trump to humiliate him repeatedly," said Republican strategist Evan Siegfried.

Trump, who attended a military academy as a teenager, has shown an affinity for generals, appointing several to key cabinet posts, including Kelly, who was initially made homeland security secretary, James Mattis as his defence secretary and H.R. McMaster as his national security adviser.

If he continues to extend that deference to Kelly, he'll be able to fulfil what Whipple argues is the "chief function" of an effective chief of staff: to challenge or question the president when it feels warranted.

"Is Trump capable of empowering a White House chief of staff to tell him what he doesn't want to hear?" Whipple said. "Because Trump needs to hear hard truths. And unless Kelly can tell him that, this will all be for naught."

He must stop the infighting

Discipline is expected to be a central theme for the new chief of staff.

Purdy said the leaks that have irked Trump so much are likely occurring because concerned staffers within the administration "are aghast by what the president is doing" and see it in the public's interest to make it known.

And if I were general Kelly, I would be demanding to review all the tweets.- Jon Schaff, political scientists

To Siegfried, the only way to plug the leaks is to have "a fully functioning and competent White House that's achieving results" without deep interpersonal conflicts. He said he was encouraged by the firing of Scaramucci, whose departure he likened to "the need to amputate a bad limb hanging on by a thread."

Scaramucci had threatened to "fire everybody" in the White House communications shop over leaks, and inflamed tensions with Priebus when he publicly accused him in a tweet of being a leaker.

Mark Updegrove, former director of the Lyndon B. Johnson Presidential Library, said that while it might have been part of Trump's managerial style to sow competition between factions and power centres in the West Wing, "those competitive forces have made for a very chaotic and disruptive White House."

Kelly is not likely to tolerate that kind of infighting.

Trump must entrust Kelly with power

By virtue of being someone put in place to control access to the president, Kelly should, in theory, be able to substantially influence the agenda, Updegrove said.

"If a president has trust in his chief of staff, and knows he has his best interests at heart, he can give him great leeway to being a gatekeeper."

On the other hand, Updegrove said that if Kelly himself is seen to attain "too much power or be recognized for that," he could fall out of favour with a president he says is "ruled by ego."

"Trump is a wild card, and it's likely that if Kelly is a threat to Trump himself, Trump might do something to pull him back," Updegrove said.

Jon Schaff, a political science professor at Northern State University in South Dakota, expects that as a pre-condition to accepting the job, Kelly would have ensured he has hiring and firing authority.

That's the kind of "grunt work" Schaff said Trump might be willing to hand over to Kelly so the president can continue to do TV appearances, rallies and soak up the adulation of crowds, allowing Kelly to become a powerful decision-maker.

"Somebody has to run the show; maybe it's Kelly who ends up doing that," Schaff said.

Kelly will have to pre-approve Trump's tweets

While Schaff has a hard time believing Trump would ever give up his smartphone, part of the chief of staff's job is to maintain messaging discipline.

"And if I were General Kelly, I would be demanding to review all the tweets" before Trump can publish them.

That kind of stopgap measure might avoid the president's habit of enacting "policy by tweet" such as his sudden announcement last week he was banning transgender people from serving in the military.

Responding to the claims that the White House is in disarray, Trump had tweeted Monday that there is "No WH chaos." With all the personnel shake-ups happening week to week, though, it's becoming difficult to see the situation as anything but.