On removing their tops, flirt and aristo quieten down (4,3)
I believe the answer is:
ease off
'quieten down' is the definition.
I can't judge whether this defines the answer.
'on removing their tops flirt and aristo' is the wordplay.
'on removing their tops' means to remove the first letter.
'flirt' becomes 'tease' (I've seen this in another clue).
'and' is a charade indicator (letters next to each other).
'aristo' becomes 'off' (I can't explain this - if you can you should give a lot more credence to this answer).
'tease' with its initial letter taken away is 'ease'.
'ease'+'off'='EASE OFF'
(Other definitions for ease off that I've seen before include "reduce tension" , "Slacken gradually" , "Slow down" , "Moderate, slacken" , "relax" .)