If the resignation of Defense Secretary Chuck Hagel augurs a move by President Obama to shake up his national security team and reconsider his strategy in crisis areas such as Syria and Ukraine, then it will be welcomed. So far, there’s not much sign of it. Mr. Hagel has been a weak leader at the Pentagon who, at least in public, has been less of a force in policy discussions than some of the generals who report to him. But his thinly disguised dismissal came after reports that he had raised sensible questions about Mr. Obama’s overly constrained approach to fighting the Islamic State.

The president’s second-term agenda of withdrawal from Afghanistan and retrenchment of the budget was overtaken by the Islamic State’s rise and Russia’s invasion of Ukraine.

Like the two defense secretaries who preceded him in Mr. Obama’s Cabinet, Mr. Hagel found himself caught between an insular White House team and military commanders who chafed at what they see as both micromanagement and the absence of a workable strategy.

These differences mean that Mr. Obama’s choice for a new defense secretary will be particularly important. What’s needed is a seasoned, independent policymaker with a genuine command of military affairs who is able to win the respect of both the generals and the White House.