The phrase "kept one's trap shut" means to remain silent or keep quiet. However, there are many other ways to express the same sentiment. Some synonyms include "held one's tongue," "kept mum," "stayed tight-lipped," "refrained from speaking," "kept silent," and "maintained a discreet silence." These phrases are especially useful when you want to convey the idea of someone keeping a secret, avoiding gossip, or showing discretion. Using different synonyms for the same phrase can also make your writing more interesting and varied. So, instead of relying on the same old phrase, try out some of these alternatives next time you need to communicate the idea of staying quiet.