President Donald Trump has, to great fanfare, remade his national-security team in recent days. But the most intriguing and consequential member of that team isn’t one of the newcomers, but rather the one who has been there all along: Defense Secretary Jim Mattis.

Mr. Mattis is the most enigmatic member of the Trump team. He’s the Iran hard-liner who defends the nuclear deal with Iran. He’s the warrior who argues for using diplomacy to address North Korea’s nuclear threat. He’s the military man who argues against allowing...