Get their mitts on the nest eggs! (6)

I believe the answer is:

clutch

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

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

(Other definitions for clutch that I've seen before include "Result of laying" , "Grasp - eggs - car pedal" , "Quantity of eggs: cling to" , "Grasp the brood of chickens" , "Grip part of the car-engine" .)

I've seen this clue in the Evening Standard.

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