Bit of hullabaloo at Hoover’s inauguration recital (4)
I believe the answer is:
oath
'inauguration recital' is the definition.
(an oath might be recited at an inauguration)
'bit of hullabaloo at hoover's' is the wordplay.
'bit of' says the answer is hidden in the clue.
'OATH' is hidden within 'hullabaloo at hoovers'.
(Other definitions for oath that I've seen before include "Sworn promise" , "Imprecation" , "Swear word" , "A curse or solemn declaration" , "It could be ruddy when minced" .)