Die from consumption? Hardly! (6)

I believe the answer is:

starve

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'die' is the definition.
(I know this)

I don't understand the remainder of the clue.

(Other definitions for starve that I've seen before include "Suffer from lack of food" , "Suffer from want of food" , "Averts (anag)" , "Without wishing, fast" , "Suffer great hunger" .)

I've seen this clue in The Independent.

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