keep something under your hat
US /kiːp ˈsʌmθɪŋ ˈʌndər jʊər hæt/
UK /kiːp ˈsʌmθɪŋ ˈʌndər jʊər hæt/

1.
to keep something a secret
:
•
Please keep this under your hat; I don't want anyone else to know yet.
•
She asked him to keep the news under his hat until the official announcement.