Small part of the administration (4)
I believe the answer is:
mini
'small' is the definition.
(thesaurus)
'part of the administration' is the wordplay.
'part of' says the answer is hidden in the clue.
'MINI' can be found hidden inside 'the administration'.
(Other definitions for mini that I've seen before include "Cult British car" , "Small (of car, skirt, disk,bar or series)" , "vehicle" , "Car; short dress" , "type of garment" .)