Husband with influence (4)
I believe the answer is:
hand
'influence' is the definition.
(thesaurus)
'husband with' is the wordplay.
'husband' becomes 'h' (abbreviation).
'with' becomes 'and'.
'h'+'and'='HAND'
(Other definitions for hand that I've seen before include "Mitt" , "Unclenched fist" , "writing" , "Worker - four inches - bunch of bananas" , "Hired worker" .)