(colloquial) Not open about one's sexual orientation, romantic orientation, or gender identity.
(colloquial, by extension) Not open about some feature of one's life; often construed with about.
She's in the closet about her gambling addiction.
She's in the gambling-addiction closet.
But helpless Pieces of the Game He plays Upon this Checker-board of Nights and Days Hither and thither moves, and checks, and slays, And one by one back in the Closet lays. Omar Khayyám
Just promise me, whatever we say Or do to each other, From now, we make a vow to just Keep it in the closet. Michael Jackson
The tap of hangers, swaying in the closet - unburdened hooks and empty drawers - and everywhere I tried to love you is yours again, and only yours. Joanna Newsom
I'm a books person. Yes, I have a Kindle. I used it for an hour and a half and put it in the closet. Andrew Wylie
Sucks to be left out of adolescence, sort of like getting locked in the closet on Venus when the sun appears for the first time in a hundred years. Junot Diaz
To have skeletons in the closet. German Proverb