Relative’s jibe when head goes missing (4)
I believe the answer is:
aunt
'relative's' is the definition.
(aunt is a kind of relative)
'jibe when head goes missing' is the wordplay.
'jibe' becomes 'taunt'.
'when head goes missing' means to remove the first letter.
'taunt' with its first letter taken off is 'AUNT'.
(Other definitions for aunt that I've seen before include "Family relative" , "Tuna (anag.)" , "Tuna for the odd relative" , "Wife of one's uncle" , "Blood relative" .)