Button up and Not let out a peep

Button up verb - Refuse to talk or stop talking; fall silent.

Not let out a peep and button up are semantically related in keep silent topic. In some cases you can use "Not let out a peep" instead a verb "Button up".

Button up and not let out a peep are semantically related in keep silent topic. You can use "Button up" instead a verb phrase "Not let out a peep".