The single best way to maintain the essential credibility of federal law enforcement would be for President Trump to name a Democrat to run the FBI.
There is a rich tradition of hiring someone from the opposition party. Democrat Jimmy Carter named Republican Judge William H. Webster to head the bureau in 1978. In the shadow of the Watergate scandal, Carter correctly concluded that naming a director from the other party would provide needed public confidence that the FBI was above politics. And so it would today.
Democrat Bill Clinton named Republican Louis Freeh as his FBI director. Vice President Al Gore would probably have continued that trend had he become president. (I know from working on transition planning that he was considering three Republican judges as possible heads of the FBI.) Gore’s judgment, like that of Carter and Clinton, was that having a Republican FBI director would prevent any suggestion of partisan favoritism and lend credibility to any investigation that rejected allegations against his administration. And, of course, President Barack Obama extended the term of one Republican FBI head, Robert Mueller, and replaced him with another Republican, James B. Comey, who had served as deputy attorney general in the preceding administration of George W. Bush.