Only cool person on the bench (7)
I believe the answer is:
justice
'person on the bench' is the definition.
(judges sit on the bench)
'only cool' is the wordplay.
'only' becomes 'just' (synonyms).
'cool' becomes 'ice' (icing is a kind of cooling).
'just'+'ice'='JUSTICE'
(Other definitions for justice that I've seen before include "Administration of law" , "Fair play" , "Fairness, legitimacy" , "right outcome" , "Judge, magistrate" .)