Dishonest better half went round Norway (4)
I believe the answer is:
bent
'dishonest' is the definition.
(thesaurus)
'better half went round norway' is the wordplay.
'better half' becomes 'bet'.
'went round' means one lot of letters goes inside another (I've seen this in other clues).
'norway' becomes 'n'.
'bet' enclosing 'n' is 'BENT'.
(Other definitions for bent that I've seen before include "Angled; corrupt" , "Morally crooked" , "Crooked - tendency" , "Dodgy" , "Out of shape, curved" .)