Defeat husband in public argument (9)
I believe the answer is:
overthrow
'defeat' is the definition.
(I've seen this before)
'husband in public argument' is the wordplay.
'husband' becomes 'h' (abbreviation).
'in' means one lot of letters goes inside another.
'public' becomes 'overt' (both can mean well-known or unconcealed).
'argument' becomes 'row' (to row is to argue).
'overt'+'row'='overtrow'
'h' put inside 'overtrow' is 'OVERTHROW'.
(Other definitions for overthrow that I've seen before include "Bring down rulers" , "Ruin" , "Error on cricket field - defeat" , "depose government" , "Fall" .)