Crossword Genius

Drunk daughter giving up anything for some ice? (7)

Ross

I believe the answer is:

drinker

I'm a little stuck... Click here to teach me more about this clue!

'drunk' is the definition.
(thesaurus)

'daughter giving up anything for some ice?' is the wordplay.
I cannot really understand how this works, but
'daughter' could be 'd' (genealogical abbreviation) and 'd' is present in the answer.
'ice?' could be 'rink' (ice is a kind of rink) and 'rink' is located in the answer.
The remaining letters 'er' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for drinker that I've seen before include "Consumer of liquid, probably alcohol" , "Tippler" , "Inebriate" , "Imbiber, toper" .)

I've seen this clue in The Independent.
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