Mark Rutte rode off into the sunset on his bicycle last week, making a carefully choreographed exit from Dutch politics, which he has dominated as prime minister for nearly 14 years. His next job will be even more challenging: He will be the new head of a NATO that is facing threats ranging from Russian aggression to the rise of right-wing nationalism across Europe.

Mr. Rutte, known as a flexible pragmatist, will bring his experience at conciliation to the 32-nation military alliance when he takes over as secretary general from Jens Stoltenberg on Oct. 1.

As it celebrates its 75th anniversary with a summit in Washington this week, NATO, which was founded to deter the former Soviet Union from further expansion in Europe, has found renewed purpose in its support for Ukraine against Russia’s invasion. Beyond that challenge, NATO faces a Russian government forging stronger ties with China and Iran, even as Beijing tries to dominate Asia and Tehran expands its nuclear program.

Leading member states like France and Germany are dealing with the empowerment of far-right parties with clear sympathies for Moscow. Hungary and Turkey are authoritarian democracies. And there are new demands to spend more money on the military.

Then there is the strong possibility that Donald J. Trump, a vocal skeptic about NATO and aid to Ukraine, will return to the White House as the leading presence in what remains an American-dominated alliance.

But Mr. Rutte, 57, has managed four difficult and different ruling coalitions in the Netherlands with aplomb, putting the need for agreement before personal ideology. He is a known quantity for other leaders, and has been praised both by President Biden, who pushed him to take the job, and by Mr. Trump, who once said after an Oval Office meeting, “I like this guy!”