Presumably have influence, holding large part of nail? (7)

I believe the answer is:

cuticle

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'part of nail?' is the definition.
'cuticle' can be an answer for 'part' (cuticle is a kind of part). I am not sure about the 'of nail?' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for cuticle that I've seen before include "Skin at foot of nail" , "layer of protection" , "Dead skin on hand" , "Skin around the nail" , "finger has one" .)

I've seen this clue in The Independent.

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