President Trump has so far restrained himself from trying to meddle with the Federal Reserve on matters related to monetary policy during his second term. But some of the more than 50 executive orders he has signed since returning to the White House are leaving an imprint on the central bank.

The latest evidence is a decision by the Fed to halt hiring for permanent workers. The central bank has removed all job postings listed on its website aside from a single summer internship opportunity.

The Fed acted after Mr. Trump mandated a governmentwide hiring freeze, ordering that no federal position vacant at that time could be filled and no new positions created. The only exemptions were granted for jobs related to military personnel, immigration enforcement, national security and public safety.

As a wholly independent organization that strives to operate apolitically, the Fed is not legally obligated to carry out decrees by the executive branch. But its decision to do so in certain cases reflects a strategy of sorts: Align with the executive branch when the Fed sees it is appropriate and lawful and, above all else, safeguard the independence of the central bank’s monetary policy decisions.

“The Fed has historically zealously guarded its independence,” said Jeremy Kress, a former Fed banking regulator who is now co-faculty director of the University of Michigan’s Center on Finance, Law & Policy. “The Fed is trying to demarcate some boundaries of executive influence.”

Jerome H. Powell, the Fed chair, touched on aspects of this approach at a news conference last week when pressed about changes taking place at the central bank since the start of Mr. Trump’s second term.