Chill current drink quickly (4,4)

I believe the answer is:

wind down

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'chill' is the definition.
(I've seen this before)

'current drink quickly' is the wordplay.
'current' becomes 'wind' (wind is a type of current).
'drink quickly' becomes 'down' (to down something can mean to drink it quickly. I am not sure about the 'quickly' bit.).
'wind'+'down'='WIND-DOWN'

Can you help me to learn more?

(Other definitions for wind down that I've seen before include "Relax after activity" , "Chill" , "Relax after stress" .)

I've seen this clue in The Times.

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