Cloak shortened as top cover (3)

I believe the answer is:

cap

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'cloak shortened as top cover' is the definition.
'cap' can be an answer for 'cloak' (thesaurus). I am not sure about the 'shortened as top cover' bit.

'cloak shortened' is the wordplay.
'cloak' becomes 'cape' (cape is a kind of cloak).
'shortened' means to remove the last letter.
'cape' with its final letter taken off is 'CAP'.

Can you help me to learn more?

(Other definitions for cap that I've seen before include "Put a limit on" , "subsidy regime" , "Beat; upper limit" , "Top; hat" , "Headgear item" .)

I've seen this clue in The Irish Independent.

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