Terror of supporter with extra time (4)
I believe the answer is:
brat
'terror' is the definition.
(synonyms)
'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' is the link.
(Other definitions for brat that I've seen before include "Ill-behaved child" , "A spoiled badly-behaved child" , "Unpleasant youngster" , "child - that's a nuisance" , "Troublesome child" .)