Cocktail and kind of pizza picked up (9)

I believe the answer is:

margarita

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'cocktail' is the definition.
(margarita is a kind of cocktail)

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

Can you help me to learn more?

(Other definitions for margarita that I've seen before include "Tequila and lime cocktail" , "Caribbean island" , "Spanish girl" , "Type of tequila cocktail" , "Stiff drink" .)

I've seen this clue in The Telegraph.

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