Dictionary

Not open about one's sexual orientation, romantic orientation, or gender identity.

(by extension) Not open about some aspect of one's identity, tendency or fondness; secret.

To shut away for private discussion.

Example: The ambassador has been closeted with the prime minister all afternoon. We're all worried what will be announced when they exit.

To put into a private place for a secret interview or interrogation.

To shut up in, or as in, a closet for concealment or confinement.

Confined.

Example: He's spent all day closeted in his room.

Sheltered, protected