Company making cuts – using gentle persuasion (7)
I believe the answer is:
coaxing
'gentle persuasion' is the definition.
'coaxing' can be an answer for 'persuasion' (thesaurus). I am not certain of the 'gentle' bit.
'company making cuts' is the wordplay.
'company' becomes 'co' (abbreviation).
'making cuts' becomes 'axing' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'co'+'axing'='COAXING'
'using' acts as a link.
Can you help me to learn more?
(Another definition for coaxing that I've seen is " Inveigling, cajoling".)