Pairs cool off in Athens landmark (9)
I believe the answer is:
acropolis
'athens landmark' is the definition.
(I've seen this before)
'pairs cool off' is the wordplay.
'off' is an anagram indicator.
'pairs'+'cool'='pairscool'
'pairscool' with letters rearranged gives 'ACROPOLIS'.
'in' acts as a link.
(Other definitions for acropolis that I've seen before include "Citadel of ancient Greece" , "Upper fortified part of Greek city as in Athens" , "old citadel" , "Imposing building" , "high point" .)