zip (something) up
Definition: to fasten something using a zip. (N.B. the opposite is ‘unzip’, not ‘zip down’)
E.g.1: The teacher wondered why the class was laughing until he noticed that he had forgotten to zip his trousers up.
E.g.2: Her suitcase was so full that she couldn’t zip it up without sitting on it.
This phrasal verb can be separated. (E.g. 1 and 2)