button (someone) up

Translations
застегнуть (кого-то) на пуговицы
She buttoned her coat up before going outside.
Она застегнула своё пальто на пуговицы перед выходом на улицу.
Definitions
To button someone up means to secure or close off a person, often in a metaphorical sense, by making them more reserved or cautious, or to ensure that they do not disclose information.