button up

fe’l verb

1. To fasten with a button or buttons. Button up your shirt cuff. It has come undone
2. To fasten all the buttons on a coat, or similar item of clothing, to keep warm. Button up well. It's freezing outside today.
3. To conclude; to finalize; to put the finishing touches (on) It's time to button up the meeting.
4. To remain silent, especially in order to keep a secret or to avoid saying something inappropriate.