Small company run heartlessly in contempt (5)
I believe the answer is:
scorn
'contempt' is the definition.
(synonyms)
'small company run heartlessly' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'company' becomes 'co' (abbreviation).
'heartlessly' means to remove the middle letters.
'run' with its centre taken out is 'rn'.
's'+'co'+'rn'='SCORN'
'in' acts as a link.
(Other definitions for scorn that I've seen before include "Open disrespect" , "Utter contempt" , "Contumely" , "Mocking contempt" , "Slight" .)