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.