New critic losing head gets push (5)

I believe the answer is:

nudge

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'push' is the definition.
(I know that nudge is a type of push)

I can't explain the rest of the clue.

(Other definitions for nudge that I've seen before include "Push gently" , "Gentle poke with elbow" , "Gentle prod" , "Light touch or push" , "Jogger" .)

I've seen this clue in The Sun.

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