This is taken from an article in The New Daily, an online Australian newspaper, which appeared in December last year. The occasion was the election of a new leader (Bill English) and deputy leader of the National Party. The newly-elected (by her party) deputy leader of the NZ National Party was Paula Bennett, referred to as “former teen solo mum Paula Bennett”.
The idiomatic expression (or metaphor) used by Paula Bennett was zip-it. You can watch the episode in which she used the expression in a clip from Parliament, linked from an article in the New Zealand Herald. There was some discussion of the appropriateness of a Minister using the expression “zip it, sweetie”, as she did, but the Speaker decided that the usage was trivial, and disallowed the comments.
There was no discussion of the pronounciation of the consonants in “zip it”, which would have aroused comment in Australia, as would the expression “a bit of a difference”, also used by the Minister.
The Auckland Herald made the expression its top quote of 2012. when the incident took place in the New Zealand Parliament.
According to the Cambridge dictionary, “zip it” is “a rude and angry way of telling someone to stop talking”, with this example given: Just zip it - I'm tired of listening to you complain. This wasn’t the interpretation given by the Speaker of the NZ Parliament. The zip (a closure device) features in quite a few idioms or metaphors, as does its verb form (“to fasten with a zip”).
The Urban Dictionary traces the term back to about 1988, when it was used by a notorious talk-show host in the United States, Morton Downey Jr.