Secret still repeated (4-4)
I believe the answer is:
hush-hush
'secret' is the definition.
(I know that secret can be written as hush-hush)
'still repeated' is the wordplay.
'still' becomes 'hush' (synonyms).
'repeated' shows that letters should be duplicated.
'hush' duplicated is 'HUSH-HUSH'.
(Other definitions for hush-hush that I've seen before include "Cloak-and-dagger, secret" , "Highly confidential" , "Be quiet, twice - it's very secret" , "Highly secret" , "Informally kept very secret - twice?" .)