Although the president appoints Fed governors, the Fed is an independent agency and the governors can be fired only "for cause." It's unclear if Trump could remove Powell as chairman while he remains a governor.
Acting White House Chief of Staff Mick Mulvaney said Sunday that President Trump “now realizes” he can’t fire Federal Reserve Chairman Jerome Powell, an acknowledgment that came after reports that Trump has discussed dismissing the Fed chief in recent days amid the stock market’s meltdown.