Shifting hair oil, American makes killing (9)
I believe the answer is:
hilarious
'killing' is the definition.
(killing can informally mean very funny)
'shifting hair oil american' is the wordplay.
'shifting' indicates anagramming the letters.
'american' becomes 'us' (abbreviation for United States).
'hair'+'oil'='hairoil'
'hairoil' is an anagram of 'hilario'.
'hilario'+'us'='HILARIOUS'
'makes' is the link.
(Other definitions for hilarious that I've seen before include "A scream" , "Extremely amusing" , "Priceless!" , "Extremely funny" , "Louis' hair! (anag)" .)