Crossword Genius

Down a drink, say, with audacity? (4)

Ross

I believe the answer is:

neck

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This could be a double definition.

'down a drink say' is the first definition.
'neck' can be an answer for 'down' (both can mean to finish a drink). I am unsure of the 'a drink say' bit.

'audacity?' is the second definition.
(neck can mean rudeness or audacity)

'with' acts as a link.

Can you help me to learn more?

(Other definitions for neck that I've seen before include "A hard one shows some nerve" , "Pet" , "jowl?" , "A short lead" , "Bottle part" .)

I've seen this clue in The Irish Times.
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