Insensitive of daughter to support removing kitchen sink (5-7)
I believe the answer is:
thick-skinned
'insensitive' is the definition.
(thesaurus)
'daughter to support removing kitchen sink' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'to support' says to put letters next to each other (in a down clue, some letters hold up others).
'removing' indicates anagramming the letters (moving the letters again).
'kitchen'+'sink'='kitchensink'
'kitchensink' is an anagram of 'thickskinne'.
'd' after 'thickskinne' is 'THICK-SKINNED'.
'of' is the link.
(Other definitions for thick-skinned that I've seen before include "Not easily hurt, upset" , "Indifferent to criticism" , "Insensitive" , "Pretty impermeable to criticism" .)