For decades, the normal course of action for presidents departing the White House has been to lie low and let their successors have the stage to themselves in their first months in office.

But Donald J. Trump was never a normal president. And less than two months after he departed Washington as a twice-impeached leader whose supporters stormed the Capitol to try to thwart the certification of a democratic election, Mr. Trump will attract a national spotlight as the final act at the Conservative Political Action Conference on Sunday.

“His presidency was unlike any other, so why would we expect his post-presidency to be like any other?” said James Carville, the Democratic strategist most associated with former President Bill Clinton’s success in 1992. When Mr. Clinton left office in early 2001, it was also as an impeached president. But Mr. Clinton took at least some time out of view before emerging with a philanthropic group that he went on to build up for years.

Of Mr. Trump, Mr. Carville said, “It would have been utterly surprising if he would have gone away and worked on a memoir or taught a Zoom class at a state university.”

Mr. Trump is set to deliver a closing speech at CPAC that is expected to be a withering critique of President Biden’s first few weeks in office, touching on topics ranging from shuttered schools to immigration policy, said an adviser, who spoke on condition of anonymity to discuss the unfinished speech.

He isn’t expected to deliver a lengthy list of his own accomplishments in office and will aim to sound more like the candidate he was in 2016 than the campaigner he was in 2020, the adviser said. And there will be some focus on the future of the Republican Party.

When former President Barack Obama left office, he was photographed kite-surfing in February 2017, a relaxed smile on his face. His predecessor, George W. Bush, made clear his disdain for Washington and his eagerness to escape it. Karl Rove, the architect of Mr. Bush’s campaign, called it “highly unusual” for a former president not to give the incoming chief executive a grace period of his own silence.

Mr. Trump has been relatively selective in speaking publicly since he left the White House, after being cautioned by advisers not to say anything that might make him a larger target for the various prosecutors considering or pursuing investigations related to him. Without his Twitter feed and the presence of reporters assigned to cover the presidency, the attention that Mr. Trump craves so deeply has been in short supply.

Yet his grip on the Republican Party remains strong. Members of Congress, fearing backlash from Mr. Trump’s voters, have made plain their desire to move past any discussion of responsibility for months of helping Mr. Trump spread the baseless claim that the election was stolen from him by shadowy forces in the Democratic Party.

He was widely hailed on the first day of the CPAC convention Friday.

“Let me tell you right now,” Senator Ted Cruz of Texas said, “Donald J. Trump ain’t goin’ anywhere.” Even Senator Mitch McConnell, the Republican leader who at one point let it be known that he might vote to convict Mr. Trump in his second impeachment trial, told Fox News this week that he would support Mr. Trump if he were to be the Republican presidential nominee in 2024.

To that end, Mr. Trump is serious at the moment about running for president a third time in 2024. While some aides expect that he ultimately won’t go through with another bid, his musings could have a chilling effect on his party.

“There was never a consideration of, Should George H.W. Bush run again?” said Matt Schlapp, the chairman of the American Conservative Union, which organizes the conference. Mr. Trump is “in a different place, and he’s also still incredibly popular with the people who voted for him.”

Mr. Trump has discussed with aides the possibility of writing a book. And he has started putting together a political operation with long-serving aides including Bill Stepien, the campaign manager at the end of 2020; Justin Clark, the counsel on his campaign; and Corey Lewandowski and David Bossie, his former campaign manager and deputy campaign manager. Brad Parscale, who was removed as the 2020 campaign manager last summer, remains in the Trump circle and is handling Mr. Trump’s email system.

Jason Miller, Mr. Trump’s senior adviser, remains close to him. And Mr. Trump’s eldest son, Donald Trump Jr., is set to take a more active role in his political organization than he previously had.

Most members of that group had an hourslong meeting on Thursday with Mr. Trump, for whom few former aides are ever permanently cast aside.

The former president is setting up a process for people looking to receive his endorsement, but he has made it clear that he is also determined to extract vengeance against Republicans who crossed him by questioning his lies about the election or by voting in support of impeachment. On Friday, he endorsed a former aide, Max Miller, as a primary challenger to Representative Anthony Gonzalez of Ohio, who voted in favor of impeachment.

What remains to be seen at CPAC is whether Mr. Trump will attempt to revive his false statements about a “rigged” 2020 election. His advisers are imploring him not to, and they say the hope is that Mr. Trump will focus on suggesting changes to election rules across the country.

Even if he doesn’t say it himself, CPAC — once a forum for conservative ideas with a strong libertarian strain — has been transformed into a cult of personality around Mr. Trump. So far at the four-day gathering, a golden statue of Mr. Trump has been pushed around the Orlando, Fla., venue, with no apparent sense of irony. The event is being held away from Washington, its customary home, because regulations intended to slow the spread of Covid-19 are more lax in Florida.

Mr. Trump’s false claims of voter fraud have already gotten a boost at the gathering; a panel titled “How Judges & Media Refused to Look at the Evidence” was conducted on Friday.

In a Wall Street Journal opinion piece, Mr. Rove wrote that Mr. Trump should steer away from his desire to discuss payback against other Republicans.

“Mr. Trump took this approach in his disastrous campaign stop the night before the Jan. 5 Georgia Senate runoffs,” Mr. Rove wrote. “If he repeats it at CPAC, he’ll be speaking to the shrinking share of the electorate that believes his every claim.” He urged Mr. Trump to take a “more constructive” approach.

Few Republicans believe that Mr. Trump has the discipline to drop his desire for attention for long, if at all. Already, he has shown flashes of behaving like the political gadfly in search of attention he was in the years leading up to his run in 2016.

When Mr. Trump was considering a bid for president as early as 2011, he used his Twitter feed and his frequent Fox News appearances to inject himself into nearly every topic in the news cycle. Mr. Trump’s advisers insist that he says he is happier without his Twitter feed.

But just a few weeks out of office, Mr. Trump has at times relied on the same impulse: getting media attention for topics in the news, such as the death of the radio host Rush Limbaugh or the car accident that felled the golfer Tiger Woods, to speak to an audience that is already supportive of him.

“In 2013 and 2014, Mr. Trump wanted ‘to be part of the action,’” recalled Sam Nunberg, a former adviser to the Trump campaign in 2016. Now, as a former president, Mr. Nunberg said, Mr. Trump “has ‘to be part of the action’ to keep his precarious grip as the leading contender for the 2024 G.O.P. primary.”

“The reality is that speaking at CPAC so soon after becoming only the 10th president to lose re-election is a sign of weakness,” Mr. Nunberg said.