Revealing little and putting it back in the new cover (8)

I believe the answer is:

reticent

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'revealing little and putting it back' is the definition.
I can't tell whether this defines the answer.

'in the new cover' is the wordplay.
'in' indicates putting letters inside.
'the new' becomes 'recent' (I've seen this before).
'cover' becomes 'ti' (I can't explain this - if you can you should believe this answer much more).
'recent' enclosing 'ti' is 'RETICENT'.

Can you help me to learn more?

(Other definitions for reticent that I've seen before include "Not wanting to talk" , "Uncommunicative" , "Quiet" , "Reserved - taciturn" , "'Self-effacing, restrained (8)'" .)

I've seen this clue in the Evening Standard.

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