Green’s Dictionary of Slang

zip one’s lip v.

also use the zipper, zip one’s mouth, …trap, zipper one’s mug, ...trap, ...yap
[SE zip + lip/mouth/mug n.1 (1d)/trap n.1 (5)]

(orig. US) to stop talking; esp. in imper.

[US]Howsley Argot: Dict. of Und. Sl. 53: use the zipper – keep the mouth shut, reveal nothing.
[US]R.L. Bellem ‘Malibu Mess’ Dan Turner – Hollywood Detective Dec. [Internet] Both of you keep your yaps zippered about what’s happened.
[US]R.L. Bellem ‘Half-Size Homicide’ in Speed Detective Nov. [Internet] My best bet was to zipper my kisser until I had a chance to snoop around.
[US]R. Service ‘Montreal Maree’ in Songs of a Sun Lover (1955) 73: Now though I zippered up my mug somehow the story spread / That I was playin’ poker and my banker was Maree.
[US](con. WWII) F.I. Gwaltney Heaven and Hell 52: I made a gesture of zipping up my mouth and Wille passed back a no-talking order.
[US]W. Brown Teen-Age Mafia 9: They played it cool [...] kept their lips zipped.
[US]P. Crump Burn, Killer, Burn! 13: Dammit, Dipper, zip your lip.
[US]M. Rumaker Exit 3 and Other Stories 66: Sam, you zipper your trap. [...] Let Carp go on and tell the story.
[US]F. Hilaire Thanatos 133: Nobody told me to keep my lip zipped.
[US]T. Alibrandi Custody 283: I want you, mentally, to turn off your hearing aid and zip up your mouth.
[US]A. Maupin Further Tales of the City (1984) 199: ‘I want this to be . . . official, Father.’ ‘Meaning, zip the old lip, huh?’.
[US]T.R. Houser Central Sl. 46: Don’t be puttin no salt in my game, zip your fat mouth and let me finish.
[US]P. Cornwell Body of Evidence (1992) 211: Sometimes he snitches a little, other times he zips his lip.
[US](con. 1964–8) J. Ellroy Cold Six Thousand 641: She said no more. She zipped her lips and played coy.
[US]T. Dorsey Cadillac Beach 189: You a news-fink? My trap’s zipped.
[UK]J.J. Connolly Viva La Madness 369: Ted nods, lips zipped.