Stick around entrance to restaurant, but go without food (6)

I believe the answer is:

starve

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'go without food' is the definition.
(I've seen this before)

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

(Other definitions for starve that I've seen before include "Die of hunger" , "Eat nothing" , "Averts (anag)" , "Stop feeding" , "Suffer from lack of food" .)

I've seen this clue in The Times.

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