Insensitive wife finally accepted by relative (4)
I believe the answer is:
dead
'insensitive' is the definition.
(thesaurus)
'wife finally accepted by relative' is the wordplay.
'finally' suggests the final letters.
'accepted by' means one lot of letters goes inside another.
'relative' becomes 'dad' (dad is a kind of relative**).
The last letter of 'wife' is 'e'.
'e' going within 'dad' is 'DEAD'.
(Other definitions for dead that I've seen before include "Unresponsive" , "No longer alive" , "Devoid of life" , "Inanimate" , "Stiff - bereft of life" .)