BRUSSELS—When NATO Secretary-General Mark Rutte took office in 2024, his biggest challenge was getting the alliance’s European members to spend more on defense. Now, with tens of billions of new dollars pouring into the continent’s militaries, the problem is how to quickly turn that money into potent weapons and more capable armed forces. “A year ago was all about promises” of additional spending, Rutte told The Wall Street Journal ahead of the planned North Atlantic Treaty Organization summit in Ankara, Turkey, this week. This year “it’s about delivery,” he said. It is a high-stakes race, with the allies caught between...