tight-lipped

adjective2

1. •
   Having the lips pressed tightly together, hence, not speaking.

   • He would have sprung upon Captain Blood, who stood aloof, alert, tight-lipped, and watchful. — 1922
2. •
   Unwilling to divulge information.

   • The open access operator has remained tight-lipped over what may have caused the driver to suddenly apply the brake, but stressed that safety was its priority. — 2022