Elderly relative housed in apartment that's gross (8)
I believe the answer is:
flagrant
'gross' is the definition.
('flagrant' can be a synonym of 'gross')
'elderly relative housed in apartment' is the wordplay.
'elderly relative' becomes 'gran' (I've seen this before).
'housed in' means one lot of letters goes inside another.
'apartment' becomes 'flat' ('flat' can be a synonym of 'apartment').
'gran' inserted inside 'flat' is 'FLAGRANT'.
'that's' is the link.
(Other definitions for flagrant that I've seen before include "Shocking" , "notorious" , "Blatant, outrageous" , "'Conspicuous, glaring (8)'" , "Crying" .)