Milk from faucet served up (3)

I believe the answer is:

tap

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'milk' is the definition.
(both can mean to exploit or use)

I can't explain the remainder of the clue.

(Other definitions for tap that I've seen before include "Light blow; draw sap from (tree)" , "Flow controller; knock" , "milk" , "water supply" , "It's faucet in the US" .)

I've seen this clue in The Sun.

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