Make it last initially until the end of the week to agitate them, and then have a drink (9)

I believe the answer is:

milkshake

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'a drink' is the definition.
(milkshake is a kind of drink)

I cannot understand how the remainder of the clue works.

(Another definition for milkshake that I've seen is " Cold whisked drink".)

I've seen this clue in The Irish Times.

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