Father abandoned by that woman? That's rich! (3)
I believe the answer is:
fat
'rich' is the definition.
(synonyms)
'father abandoned by that woman?' is the wordplay.
'abandoned by' is a deletion indicator.
'that woman?' becomes 'her' (pronoun for a woman).
'father' with 'her' removed is 'FAT'.
'that's' is the link.
(Other definitions for fat that I've seen before include "Corpulent; little (chance)" , "Substantial" , "Portly" , "Cooking grease" , "Obese, having spare tyre etc" .)