Cover on centre intended to protect pupil (6)

I believe the answer is:

eyelid

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'pupil' is the definition.
(thesaurus)

'cover on centre' is the wordplay.
'cover' becomes 'lid' (lid is a kind of cover).
'on' says to put letters next to each other.
'centre' becomes 'eye' (synonyms).
'lid' after 'eye' is 'EYELID'.

'intended to protect' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for eyelid that I've seen before include "Optical membrane" , "Ocular closer" , "Natural optic protector" , "Natural optic covering" , "Blinking membrane" .)

I've seen this clue in The Guardian.

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