Lest, perhaps, the hand coming through should frighten you (7)

I believe the answer is:

startle

I'm a little stuck... Click here to teach me more about this clue!

'frighten you' is the definition.
'startle' can be an answer for 'frighten' (I've seen this before). I'm not sure about the 'you' bit.

I can't explain the remainder of the clue.

Can you help me to learn more?

(Other definitions for startle that I've seen before include "Surprise with starlet" , "Rattles (anag.)" , "Shock (someone)" , "Alarm (someone)" , "Frighten suddenly" .)

I've seen this clue in the Evening Standard.

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