Drink first of sherries, something going to one's head (4)

I believe the answer is:

swig

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'drink' is the definition.
(I know that swig is a type of drink)

I cannot understand how the rest of the clue works.

(Other definitions for swig that I've seen before include "Gulp of drink" , "Drink in large draughts" , "Swallow drink hurriedly" , "Swallow (drink) greedily" , "Drink (a deep draught)" .)

I've seen this clue in The Guardian.

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