In his first week on the job, General McMaster has already shown an independence familiar to past colleagues. He has begun moving to revise an organizational order issued last month that seemed to downgrade the role of the chairman of the Joint Chiefs and the director of national intelligence, and he told an all-hands staff meeting that he did not consider the term “radical Islamic terrorism” helpful, even as the president insists on using it.

But those are relatively small matters compared to what may come. Already, Defense Secretary Jim Mattis, a retired four-star Marine general, has led the president to put aside his desire to reinstitute torture in interrogations of terrorism suspects, at least by the military. Mr. Trump places great faith in the generals he has surrounded himself with, but he and General McMaster had never met until a week ago, and the book’s reputation may set a hard-to-meet standard for the general.

“The difficulty is that Trump has a lot of crazy ideas in his head — like we should steal Iraq’s oil or we should kill the relatives of terrorists or we need to ban Muslims from coming here,” said Max Boot, a military historian at the Council on Foreign Relations. “And I’m sure someone like McMaster, like Mattis, understands how crackpot these ideas are.

“So can you say to the president, ‘Hey, Sir, you’re full” of it? Mr. Boot continued. “Or do you have to sugarcoat it and handle him with kid gloves? I suspect it’s the latter, and that’s not been H. R.’s approach. We’ll see if Trump is man enough to take it.”