"Give the quietus" is an idiomatic expression that means to put an end to something or to bring it to a close. There are many synonyms that can be used in place of this phrase. Some of the most commonly used alternatives include "finish off," "put to rest," "conclude," "terminate," "cease," "halt," "bring to a conclusion," "put the kibosh on," "quash," "suppress," "extinguish," "eliminate," "halt in its tracks," "end," "put an end to," and "put a stop to." Ultimately, the choice of synonym will depend on the specific context in which the phrase is being used and the tone and style of the speaker/writer.