Actually, the FBI director is supposed to be non partisan. That is why his term is 10 years - he’s not supposed to be a political appointee such as the Sec of Transportation. He can only be fired for cause and not because there is a change in presidents. Clinton fired Sessions, who Reagan appointed as FBI Director, I think in Clinton’s first year, but Sessions was under an ethics investigation courtesy of, guess who, William Barr before he left office at the end of Bush Sr term. So that gave Clinton cover to fire him. Clinton nominated Louis Freeh, a republican to the FBI top position and he resigned in 2001 under pressure from Congress because of foreign spying incidents. He was followed by Mueller, who served 12 years because Congress extended 2 years to his term. So, it’s not a partisan position that changes when a different president takes office.
Correction, wasn’t a partisan position. Like most parts of the federal government, the FBI has been corrupted into pure partisanship in favor of the left by the Deep State.