Chief's armpit not fresh (9)
I believe the answer is:
important
'chief's' is the definition.
('important' can be similar in meaning to 'chief')
'armpit not fresh' is the wordplay.
'fresh' indicates an anagram.
'armpit'+'not'='armpitnot'
'armpitnot' anagrammed gives 'IMPORTANT'.
(Other definitions for important that I've seen before include "Main" , "Of significance or value" , "Leading" , "A priority" , "Crucial" .)