Former husband has to lie about banishment
I believe the answer is:
exile
'banishment' is the definition.
(exile is a kind of banishment)
'former husband has to lie about' is the wordplay.
'former husband has' becomes 'ex' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'about' is an anagram indicator.
'lie' is an anagram of 'ile'.
'ex'+'ile'='EXILE'
Can you help me to learn more?
(Other definitions for exile that I've seen before include "Send away" , "Person forced from country" , "Ousted person" , "One barred from their native country" , "Deportee" .)