Persuaded firm to cut down (6)
I believe the answer is:
coaxed
'persuaded' is the definition.
(coaxing is a kind of persuading)
'firm to cut down' is the wordplay.
'firm' becomes 'co' (a firm is a company).
'to cut down' becomes 'axed' (I've seen this before).
'co'+'axed'='COAXED'
(Other definitions for coaxed that I've seen before include "Induced" , "Persuaded gently" , "Cajoled, persuaded with soft talk" , "Wheedled, cajoled" , "Persuaded by fondling or flattery" .)