Relative lean and haggard? Not good (4)
I believe the answer is:
aunt
'relative' is the definition.
(aunt is a kind of relative)
'lean and haggard? not good' is the wordplay.
'lean and haggard?' becomes 'gaunt' (I've seen this before).
'not' suggests deleting specific letters.
'good' becomes 'g' (abbreviation).
'gaunt' with 'g' taken out is 'AUNT'.
(Other definitions for aunt that I've seen before include "Family member" , "Uncle's wife" , "Put up with" , "Close relative" , "Charley's in play?" .)