As secretary of state, Mr. Pompeo will also have to navigate the rivalries within the Trump administration. At the White House, John R. Bolton, the administration’s third national security adviser in a little over a year, is presiding over another purge of top assistants. Mr. Pompeo must forge a working relationship with Mr. Bolton as he creates alliances with the White House chief of staff, John F. Kelly; Defense Secretary Jim Mattis; and Mr. Kushner.

Mr. Pompeo’s early military career — he attended West Point and became a tank commander before leaving for Harvard Law School — could endear him to Mr. Kelly and Mr. Mattis, both former four-star generals.

But handling Mr. Kushner will be a delicate matter. Mr. Kushner’s diplomatic portfolio includes forging a Middle East peace deal and safeguarding the relationship with Mexico even as Mr. Trump pursues his hard-line immigration policies and wall on the southern border with Mexico.

Mr. Pompeo will also have to mend fences with the American ambassador to the United Nations, Nikki R. Haley, whose relationship with Mr. Tillerson was so strained that she ordered his portrait removed from her New York offices. She was absent from this week’s state dinner with President Emmanuel Macron of France.

Mr. Pompeo’s year of service as the director of the C.I.A. has given him a running start. He forged an unlikely bond with Mr. Trump while giving the president daily intelligence briefings. The trust between them is so strong that Mr. Trump sent Mr. Pompeo to Pyongyang last month on a secret trip to pave the way for a high-stakes summit meeting with the North Korean leader, Kim Jong-un, now expected to take place in June.

But first, Mr. Pompeo must deal with Russia.

Within hours of his landing in Europe, he will preside over a breakfast meeting at NATO Headquarters to discuss new measures to counter an increasingly aggressive Russian president, Vladimir V. Putin, who American intelligence officials say ordered the annexation of Crimea, the intervention in Ukraine, the hacking of the American election in 2016 and the murders or attempted murders of countless rivals, including a former Russian spy living in Britain. He has maintained his military and diplomatic support for President Bashar al-Assad of Syria despite the massacre of civilians and the use of chemical weapons.