Any private area, (particularly) bowers in the open air.
Any private or inner room, (particularly):
A pew or side-chapel reserved for a monarch or other feudal lord.
A private cabinet, (particularly):
Any small room or side-room, (particularly):
An ordinary similar to a bar but half as broad.
A sewer.
To shut away for private discussion.
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.
Private.
Secret, (especially) with reference to gay people who are in the closet; closeted.