Wiktionary
vb. (alternative form of zip one's lip English)
Usage examples of "zip it".
They would fit if I didn't zip it, but that meant my stockings were gonna be ruined.
If Doris Arthur came through with the script ahead of schedule, he could zip it over in a Poseidon wallet within twenty-four hours.
She went on to explain in detail how she had finally waited out in the hallway of the motel until some nice Arab man had passed by and helped her unzip her dress so she could start all over again and zip it up without getting snagged on chiffon.
The Humphrey/Muskie axis had been desperately trying to put something together with aging diehards like Wilbur Mills, George Meany, and Mayor Daley -- hoping to stop McGovern just short of 1400 -- but on the weekend after the New York sweep George picked up another fifty or so from the last of the non-primary state caucuses and by Sunday, June 25th, he was only a hundred votes away from the 1509 that would zip it all up on the first ballot.