WASHINGTON—When Mike Pompeo was confirmed as secretary of state 16 months ago, he was considered the last puzzle piece to President Trump’s overhauled foreign policy team. Now, he’s the last one remaining.

The sudden departure on Tuesday of John Bolton as the president’s national security adviser—a strong personality and unique character even by Trumpian standards—removed one of the last dissenting voices in the West Wing. It also immediately empowered Mr. Pompeo, already one of the longest-tenured and most trusted foreign-policy...