Husband that’s horrible — this chap? (4)
I believe the answer is:
hugh
'chap?' is the definition.
'husband that's horrible' is the wordplay.
'husband' becomes 'h' (abbreviation).
'that's horrible' becomes 'ugh' (expression of disgust).
'h'+'ugh'='HUGH'
'this' is the link.
(Other definitions for hugh that I've seen before include "man!" , "Middle name of WH Auden" , "W.H. Auden's middle name" , "- Grant, British actor" .)