1. Literally, to have one's lips pressed together, as in anger. I knew my girlfriend was angry as soon as I saw that she was tight-lipped and glaring at me.
2. To be unwilling to talk openly or share details about someone or something. I still don't know anything about Maria's new boyfriend because she's so tight-lipped about him. Don't worry, we can trust my sister to be tight-lipped—she won't tell anyone about our engagement until we do.