tight-lipped 
adjective
With the lips firmly closed, especially as a sign of suppressed emotion or determined reticence: she stayed tight-lipped and shook her head...
- I had hoped many tight-lipped elite military officers would speak sincerely about their role in the riots.
- In consequence we are becoming a tight-lipped silent majority afraid to rise above the parapet.
- As with his magic secrets Gold remains tight-lipped about his next venture.
Synonyms
reticent, taciturn, uncommunicative, unforthcoming, unresponsive, close-mouthed, close-lipped;
silent, quiet, unspeaking;
guarded, secretive, private, withdrawn, playing one's cards close to one's chest, of few words, untalkative
informal mum