button up

/B AH1 T AH0 N AH1 P/
verb
  1. 1

    To remain silent, especially in order to keep a secret or to avoid saying something inappropriate.

verb
  1. 1

    To fasten with a button or buttons.

    โ€œButton up your shirt cuff. It has come undoneโ€

  2. 2

    To fasten all the buttons on a coat, or similar item of clothing, to keep warm.

    โ€œButton up well. It's freezing outside today.โ€

  3. 3

    To conclude; to finalize; to put the finishing touches (on)

    โ€œIt's time to button up the meeting.โ€

  4. 4

    To seal off (a military vehicle or facility).

Source: https://en.wiktionary.org/wiki/button%20one's%20lip, https://en.wiktionary.org/wiki/button%20up, https://en.wiktionary.org/wiki/button%20up%20one's%20lip