Crossword Genius

Thirsty bird I supplied with cocktail (3,7)

Ross

I believe the answer is:

dry martini

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

'cocktail' is the definition.
(I've seen this before)

'thirsty bird i supplied' is the wordplay.
I cannot quite see how this works, but
'thirsty' could be 'dry' (similar in meaning) and 'dry' is found in the answer.
'bird' could be 'martin' (martin is a kind of bird) and 'martin' is found within the answer.
'i' is within the answer.
No letters remain.
This may be the basis of the clue (or it may be nonsense).

'with' acts as a link.

Can you help me to learn more?

(Other definitions for dry martini that I've seen before include "drink" , "Gin-based cocktail" .)

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