When Robert S. Mueller III, the first special counsel to investigate Donald J. Trump, concluded his investigation into the ties between Mr. Trump’s 2016 campaign and Russia, his report raised questions about whether Mr. Trump had obstructed his inquiry.

Justice Department officials and legal experts were divided about whether there was enough evidence to show Mr. Trump broke the law, and his attorney general — chosen in part because he was skeptical of the investigation — cleared him of wrongdoing.

Four years after Mr. Mueller’s report was released, Jack Smith, the second special counsel to investigate Mr. Trump, added new charges on Thursday to an indictment over his handling of classified documents, setting out evidence of a particularly blatant act of obstruction.

The indictment says that just days after the Justice Department demanded security footage from Mar-a-Lago, his residence and private club in Florida, Mr. Trump told the property manager there that he wanted security camera footage deleted. If proved, it would be a clearer example of criminality than what Mr. Mueller found, according to Andrew Goldstein, the lead investigator on Mr. Mueller’s obstruction investigation.

“Demanding that evidence be destroyed is the most basic form of obstruction and is easy for a jury to understand,” said Mr. Goldstein, who is now a white-collar defense lawyer at the firm Cooley.

“It is more straightforwardly criminal than the obstructive acts we detailed in the Mueller report,” he said. “And if proven, it makes it easier to show that Trump had criminal intent for the rest of the conduct described in the indictment.”

The accusation about Mr. Trump’s desire to have evidence destroyed adds another chapter to what observers of his career say is a long pattern of gamesmanship on his part with prosecutors, regulators and others who have the ability to impose penalties on his conduct.

And it demonstrates how Mr. Trump viewed the conclusion of the Mueller investigation as a vindication of his behavior, which became increasingly emboldened — particularly in regards to the Justice Department — throughout the rest of his presidency, a pattern that appears to have continued despite having lost the protections of the office when he was defeated in the election.

In his memoir of his years in the White House, John R. Bolton, who served as Mr. Trump’s third national security adviser, described Mr. Trump’s approach as “obstruction as a way of life.”

In the hours after the new charges became public, Mr. Trump, whose advisers have been blunt that he must win the election to overcome his legal challenges, highlighted the stakes for him of the 2024 election.

He suggested in an interview with a right-wing news site that if he is elected, he will use the powers of the presidency to insulate himself from legal accountability on the documents case and the other inquiry being conducted by Mr. Smith into Mr. Trump’s efforts to retain power after his 2020 election loss.

“I wouldn’t keep him,” Mr. Trump told Breitbart, the news site, in response to a question about whether he would fire Mr. Smith. “Jack Smith? Why would I keep him?”

The new charges show how even in the face of Justice Department scrutiny into whether he still had classified documents in his possession, Mr. Trump has continued to try to find ways to upend its investigation.

In June of last year, in the midst of its efforts to retrieve classified material Mr. Trump had taken from the White House upon leaving office, the Justice Department served a grand jury subpoena on Mr. Trump’s organization for surveillance footage from Mar-a-Lago that would show how boxes of the documents had been handled, especially around a storage room where many of them had been stashed.

Shortly after the Trump Organization received the subpoena, the revised indictment said, the former president called Mar-a-Lago’s property manager and head of maintenance, Carlos De Oliveira. The two men spoke for 24 minutes, prosecutors say.

Two days later, Mr. De Oliveira and another defendant in the case, Mr. Trump’s valet, Walt Nauta, “went to the security guard booth where surveillance video is displayed on monitors, walked with a flashlight through the tunnel where the storage room was located, and observed and pointed out surveillance cameras.”

Days later, Mr. De Oliveira had a private conversation with the Mar-a-Lago employee in charge of the surveillance footage. The conversation was supposed to “remain between the two of them,” according to the charging document.

Mr. De Oliveira told the employee that “‘the boss’ wanted the server deleted,” the indictment said.

The employee in charge of the footage said “that he would not know how to do that, and that he did not believe that he would have the rights to do that.”

But Mr. De Oliveira continued to push, asking, “What are we going to do?” (The Trump Organization ultimately turned over security footage, but, as The New York Times reported in May, investigators became suspicious about whether someone in Mr. Trump’s orbit tried to limit the amount of footage given to the government.)

The updated indictment also demonstrates how Mr. Trump, in the aftermath of the search of Mar-a-Lago last August, turned to an issue that he obsessed about in the White House: loyalty.

“Someone just wants to make sure Carlos is good,” the indictment quoted Mr. Nauta as saying about Mr. De Oliveira to another Trump employee.

That employee told Mr. Nauta that Mr. De Oliveira was “loyal” and “would not do anything to affect his relationship with Mr. Trump.”

Shortly after that exchange, Mr. Trump called Mr. De Oliveira and said that he would get him a lawyer, the indictment said. Legal fees for Mr. De Oliveira, Mr. Nauta and other Trump employees who have become witnesses or defendants in the documents case are being paid by a political action committee affiliated with Mr. Trump.

Mr. Trump’s desire for loyalty echoed behavior that Mr. Mueller captured in his report, which laid out how Mr. Trump asked the former F.B.I. director, James B. Comey, for his loyalty just days after taking office. Mr. Comey continued to pursue an investigation into ties between Mr. Trump’s campaign and Russia and was fired in Mr. Trump’s fifth month in office. Mr. Mueller was appointed as special counsel in the aftermath of Mr. Comey’s dismissal.

Mr. Mueller’s investigation ultimately identified nearly a dozen acts Mr. Trump took that could be seen as obstruction of justice. One of the most damning related to how Mr. Trump pressured his White House counsel, Donald F. McGahn II, to create a fake document rebutting statements he gave to Mr. Mueller’s office. Mr. McGahn refused to go along with what Mr. Trump wanted.

Another example related to Mr. Trump’s powers as president. During Mr. Mueller’s investigation, several of his allies and associates — including Michael Flynn and Paul Manafort — were indicted by the Justice Department in cases that could have produced damaging testimony about Mr. Trump and his campaign. As the prosecutions of the men went forward, Mr. Trump publicly dangled the idea of issuing pardons. In the final weeks of Mr. Trump’s presidency, he pardoned them.

“There are all sorts of ways to obstruct an investigation, but not every one has an equal impact,” said Brandon Van Grack, a former prosecutor on Mr. Mueller’s team. “Hiding and lying are damaging, but prosecutors can often still get at the truth. Destruction is often looked at seriously because it’s permanent. It’s permanently deleting or destroying” evidence in the case.

Steven Cheung, a spokesman for Mr. Trump, assailed the investigations into the former president’s conduct, saying “the weaponized justice system along with their Democrat allies have failed at every turn because they are on the wrong side of the facts. History will judge them harshly.”

Over many decades before reaching the White House, Mr. Trump engaged in gamesmanship with prosecutors, regulators and officials who had authority in aspects of the industries in which he operated. He lived in a New York City where corruption touched aspects of the political and government establishments and the real-estate construction businesses, and he came to believe that everything could be worked out through some kind of deal, associates and former employees said.

He courted officials who had prosecutorial jurisdiction in New York City, including Rudolph W. Giuliani, then the U.S. attorney in the Southern District of New York, and Robert Morgenthau, the district attorney in Manhattan. Faced with massive amounts of civil litigation, his impulse, former employees said, was to find lawyers who knew the judge.

In April 2018, an aspect of the Russian investigation spun off into a separate one into Michael D. Cohen, a lawyer for the Trump Organization who also served as a fixer for Mr. Trump and knew many of his secrets. After Mr. Cohen’s hotel, apartment and office were searched by the F.B.I. that month, Mr. Trump called Mr. Cohen with a message: stay strong.

He then predicted on Twitter that Mr. Cohen would never “flip” on him. Mr. Cohen eventually did provide prosecutors with information about Mr. Trump’s hush-money payments before the 2016 election to a porn star who said she had a sexual liaison with him. He later said that Mr. Trump spoke in “code” to avoid plainly communicating his desires.

Mr. Bolton, Mr. Trump’s former national security adviser, wrote in his book, “The Room Where It Happened,” that Mr. Trump repeatedly sought to interfere with law enforcement and other official actions involving foreign leaders.

During an investigation into Halkbank, a state-financed institution based in Turkey that was facing an investigation by U.S. officials for a scheme to evade sanctions on Iran, Mr. Trump told the country’s leader that he would “take care of things,” Mr. Bolton wrote.

In a brief interview on Friday, Mr. Bolton pointed to a specific aspect of Mr. Trump’s view of how the rules apply to him: his use of government power for his personal and political benefit while in office.

He cited Mr. Trump’s efforts to solicit damaging information about the Bidens from Ukraine as he withheld military aid to that country. “It shows as president he had fundamental difficulty distinguishing himself from the government,” Mr. Bolton said. “And it’s also why he couldn’t understand why government officials weren’t personally loyal to him.”

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