Reticent, secretive (5-6)
I believe the answer is:
tight-lipped
I believe this clue is a double definition.
'reticent' is the first definition.
(thesaurus)
'secretive' is the second definition.
(I've seen this before)
(Other definitions for tight-lipped that I've seen before include "Determinedly reticent" , "Uncommunicative" , "Taciturn" .)