WASHINGTON — On one foreign policy issue after another, John R. Bolton was the in-house skeptic who checked President Trump’s most unorthodox instincts. Whether it was talking to North Korea, cooperating with President Vladimir V. Putin of Russia or inviting the Taliban to Camp David, he was the national security adviser who said no.
Mr. Bolton’s exit from the West Wing on Tuesday removes one of the last constraints on Mr. Trump’s sense of the possible in world affairs. In not quite three years in the White House, Mr. Trump has cycled through more senior foreign policy and national security advisers than any other president, leaving him without the men who once were considered the adults in the room: Jim Mattis, Rex W. Tillerson, H. R. McMaster, John F. Kelly and more.
“The departure of Bolton suggests that President Trump is going to be his own foreign policy adviser,” said Martin S. Indyk, a fellow at the Council on Foreign Relations who served as a diplomat and National Security Council official during the Clinton administration.
And no matter who replaces Mr. Bolton, “it’s not going to be an important position anymore — there really isn’t going to be much of a process under Trump,” said Eliot A. Cohen, who worked for Secretary of State Condoleezza Rice during the administration of President George W. Bush.
“It’s going to be whatever is most conducive to his re-election,” Mr. Cohen said.
Mr. Bolton followed the Cold War model of foreign policy, but to an extent that Democrats and some moderate Republicans found to be extreme. He advocated strikes against Iran and Syria after the Iraq war, called for the “end of North Korea” and most recently said the United States must be more forceful in confronting the Venezuelan government.
Still, he was firmly tied to the Republican foreign policy establishment.
Mr. Trump came into office with a completely unconventional foreign policy that combined an instinctive isolationism with theatrical attempts at deal-making. And he has shown himself to be uninterested in working through the alliances that largely defined 50 years of bipartisan American foreign policy.
Mr. Trump’s diplomacy of showmanship has produced few big successes beyond a precedent-breaking series of meetings with the North Korean leader, Kim Jong-un, and declaring the defeat of the Islamic State caliphate in Syria and Iraq.
To make headway in negotiations, Mr. Trump will almost certainly have to soften some of his absolutist foreign policies. That means returning to peace talks with the Taliban — even though Mr. Trump declared that process “dead” on Monday.
In North Korea, that could mean a phased rollback of its nuclear abilities instead of an immediate and full denuclearization, as the Trump administration has demanded.
And in dealing with Iran, American officials may need to ease a “maximum pressure” campaign of bruising economic sanctions before President Hassan Rouhani will agree to meet with Mr. Trump — perhaps as soon as this month at the annual United Nations General Assembly in New York.
Mr. Bolton would have opposed all of those moves. But Secretary of State Mike Pompeo, now the senior national security official on Mr. Trump’s team, is not likely to stand in the president’s way. .
It is not known what Mr. Pompeo — or Mr. Trump, for that matter — will do to resolve a range of intractable problems, including peace between Israel and the Palestinians. Israel holds elections next week that could determine the fate of Mr. Trump’s ally, Prime Minister Benjamin Netanyahu, after which the White House has promised to release its long-awaited blueprint.
Mr. Trump also has no clear endgame for his trade fight with China, and must find a way to reconcile his staunch refusal to back down with the risk that higher tariffs will spoil the economic growth on which his re-election largely depends.
Mr. Pompeo has taken pains to ensure that he is marching firmly in step with his commander in chief. Mr. Bolton’s ouster — which he insists was a resignation — will further enhance Mr. Pompeo’s substantial influence over Mr. Trump’s foreign policy, even at the risk of overriding his own hawkish impulses.
It was Mr. Pompeo who directed and oversaw the special envoy who conducted months of peace talks with the Afghan Taliban, a process Mr. Trump called off last week but may yet resume. Mr. Bolton saw no reason to negotiate with the Afghan insurgent group, which harbored the Qaeda leader Osama bin Laden. It was opposition to Mr. Trump’s effort to strike a peace deal that was Mr. Bolton’s ultimate undoing.
Mr. Bolton “understands the world for what it is and the dangers that threaten America’s national security interests,” Senator Lindsey Graham, Republican of South Carolina, said on Twitter.
And as impulsive and unpredictable as the president’s actions may be, firing Mr. Bolton reveals a certain consistency in Mr. Trump’s worldview: Though attracted to never-been-done theatrics like bringing the Taliban to Camp David or meeting with Mr. Kim, the president is also moored by suspicion of military adventures and has a huge appetite for deals.
What Mr. Trump really wants from his foreign policy is a diplomatic victory as he heads into his 2020 re-election campaign.
“The irreconcilable difference between Bolton and Trump was that Bolton fundamentally doesn’t believe in diplomacy with adversaries, and President Trump seeks diplomacy with adversaries as must-see TV,” said Jake Sullivan, a top Democratic adviser to Secretary of State Hillary Clinton and Vice President Joseph R. Biden Jr.
He said Mr. Pompeo “is much more deferential to the president, and more interested in cultivating a good relationship with the president than sticking to his ideological guns.”
Among Mr. Trump’s national security team, Mr. Pompeo is now widely considered the first among equals.
At least three contenders mentioned on Tuesday to replace Mr. Bolton — the Iran envoy Brian H. Hook; Stephen E. Biegun, the United States’ special representative for North Korea; and Richard Grenell, the ambassador to Germany — are among Mr. Pompeo’s top lieutenants at the State Department.
But should Mr. Trump again look for a scapegoat should his foreign policy founder, Mr. Pompeo has an exit strategy — the prospect of running for the Senate from his adopted home state of Kansas, as Republican Party leaders are lobbying him to do. Mr. Pompeo has brushed off the political campaign by maintaining that he will remain at the State Department as long as Mr. Trump wants, but he has not shut the door on entering the race, according to Republicans who have spoken with him about running.
For now, “Pompeo is not going to allow for any daylight to show between himself and the president,” Mr. Indyk said. “What we are going to see now is Trump unplugged — and God knows where that is going to lead America.”
The president said he would name a new national security adviser next week.
“It’s hard for me to imagine Trump not choosing someone whose only agenda is to carry out the president’s agenda,” said Matthew C. Waxman, who held multiple national security posts in the George W. Bush administration and is now a law professor at Columbia University. “And it’s hard for me to imagine someone taking the job without that idea in mind.”