Coolidge's successor (6)
I believe the answer is:
hoover
'coolidge's successor' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for hoover that I've seen before include "Clean with vacuum cleaner" , "J Edgar . . . . . . was FBI chief" , "J Edgar ...... was FBI boss." , "US president, 1929-33" , "Vacuum cleaner of the old American president" .)