Small portion of administration (4)
I believe the answer is:
mini
'small' is the definition.
(short for miniature)
'portion of administration' is the wordplay.
'portion of' says the answer is hidden in the clue.
'MINI' can be found hidden inside 'administration'.
(Other definitions for mini that I've seen before include "(Car etc) of small size" , "Iconic economy car (introduced in 1959)" , "Short skirt - small car" , "Little - car" , "Brief" .)