General:
* As quiet as a mouse
* As tight-lipped as a clam
* As hidden as a secret
* As mysterious as a fog
* As furtive as a shadow
* As guarded as a fortress
* As subtle as a whisper
* As silent as the grave
More specific:
* Like a spy with a hidden agenda
* Like a magician guarding a secret trick
* Like a treasure chest with a locked lid
* Like a locked diary filled with secrets
* Like a whisper in the wind
The best simile will depend on the specific context and the tone you want to convey.