If what someone says or does starts tongues wagging, it causes other people to start talking and guessing things about their private lives.

Do you think if we leave the party together it will set/start tongues wagging? 你觉得如果我们俩一起离开聚会的话会惹人嚼舌头吗？

They tried to keep their affair secret, but it wasn't long before tongues began to wag. 他们试图不让别人知道他们的暧昧关系，但是不久就有了闲言碎语。