If you want a drink, move fast (3)

I believe the answer is:

nip

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'drink move fast' is the definition.
'nip' can be an answer for 'drink' (I've seen this before). I am not certain of the 'move fast' bit.

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for nip that I've seen before include "(Give) a small sharp bite" , "Light bite" , "Touch of frost" , "Pinch; bite" , "Quick, sharp, bite" .)

I've seen this clue in the Evening Standard.

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