Horror of supporter with extra time (4)
I believe the answer is:
brat
'horror' is the definition.
(both can mean a misbehaving child)
'supporter with extra time' is the wordplay.
'supporter' becomes 'bra' (a bra gives support to breasts).
'with extra' says to put letters next to each other.
'time' becomes 't' (abbreviation).
'bra'+'t'='BRAT'
'of' acts as a link.
(Other definitions for brat that I've seen before include "Spoilt child" , "Annoying child" , "Young rascal" , "Ill-mannered child" , "Nasty little kid" .)