Yes, the President May Fire the FBI Director
The first is J.Edgar Hoover. After his legendary (and notorious) 43-year tenure, Congress and the Ford White House decided that such awesome power should not be in a single set of hands for so long. In 1976, a law was enacted limiting the director’s term to ten years.
Why ten years? That brings us to the second explanation: the aspiration that law-enforcement should be apolitical and non-partisan. By settling on a ten-year limit, two years longer than any president may serve, lawmakers signaled a preference for the FBI director to be retained, even when presidential administrations change, regardless of party.
Understand, though: This is a preference, it is not binding on the president. Presumptively, after being confirmed, the FBI director is retained by subsequent presidents. If the president decides to make a change, however, the president is constitutionally authorized to remove the director and does not need cause – at least not legally (political need is always a different calculation).
Since Congress imposed the ten-year limitation, one FBI director has been removed: Director William Sessions was fired by President Clinton in 1993 after he refused to resign. It turns out, moreover, that the limit is not much of a limit: In 2011, when President Obama wanted to keep Director Robert Mueller for an extra two years, Congress accommodated him by enacting legislation extending the term. It was when Mueller’s term ended that Director James Comey was appointed in 2013.
Presumptively, Director Comey would serve until September 4, 2023. But that is only if the current president and any future president between now and then chooses to retain him.