Quiet pair revealing secret (4-4)
I believe the answer is:
hush-hush
'secret' is the definition.
(I know that secret can be written as hush-hush)
'quiet pair' is the wordplay.
'quiet' becomes 'hush' (hush can mean still or quiet).
'pair' shows that letters should be duplicated.
'hush' doubled is 'HUSH-HUSH'.
'revealing' acts as a link.
(Other definitions for hush-hush that I've seen before include "Highly secret" , "Cloak-and-dagger, secret" , "Clandestine" , "Highly confidential" , "Very secret - say it twice" .)