Care for chief isn't commonly included (8)
I believe the answer is:
maintain
'care for' is the definition.
(thesaurus)
'chief isn't commonly included' is the wordplay.
'chief' becomes 'main' (synonyms).
'isn't commonly' becomes 'ain't' (I've seen this in another clue).
'included' is an insertion indicator.
'main' going around 'aint' is 'MAINTAIN'.
(Other definitions for maintain that I've seen before include "Keep (a building) in good condition" , "Keep up - carry on" , "Profess" , "Continue with an opinion" , "Keep in a certain state" .)