Discreet; tight-lipped — someone who doesn't easily reveal secrets or talk carelessly.
彼は口堅いので、重要な案件の情報を安心して任せられる。
He's discreet, so you can trust him with important information.
口堅い同僚がいるとチーム内の信頼が高まる。
Having a discreet colleague increases trust within the team.
彼女は噂話に興味がない上に口堅いので、相談相手として適している。
She isn't interested in gossip and is tight-lipped, so she's suitable as someone to confide in.