“Trump has created a giant vacuum at the Department of Defense on the civilian side,” said Eric Edelman, a former senior Pentagon official under George W. Bush. “Nature abhors a vacuum — and so does politics.”

But as the debate over the strike showed, the uncompromisingly hawkish views Mr. Pompeo holds on Iran are starting to clash with the perspective of a president deeply skeptical of military entanglements, especially in the Middle East.

Mr. Pompeo is unlikely to publicly signal frustration with the president. Some officials say he would work through the bureaucracy to push his policy goals while on the surface sticking to the role of loyal soldier, if only because he harbors political ambitions for which Mr. Trump’s support would be invaluable. Despite Mr. Pompeo’s insistence that he has “ruled out” a Senate run next year in Kansas, many Trump administration officials expect him to enter the race.