Plays with the rate of exchange (7)
I believe the answer is:
theatre
'plays' is the definition.
(I've seen this before)
'with the rate of exchange' is the wordplay.
'with' is a charade indicator (letters next to each other).
'of exchange' indicates an anagram (I've seen 'exchange' mean this).
'rate' with letters rearranged gives 'atre'.
'the'+'atre' is 'THEATRE'.
(Other definitions for theatre that I've seen before include "eg The Globe" , "Building for the dramatic arts" , "stage productions" , "Room for surgery" , "Hospital operating room - playhouse" .)