"Heaves a sigh of relief" is a common phrase that represents the feeling of being relieved after a stressful or worrying situation. There are a few other synonyms for this phrase that can help express the same feeling, such as "exhales a breath of relief," "lets out a sigh of contentment," "breathes a sigh of ease," or "emits a sigh of satisfaction." All of these phrases represent the physical reaction to the emotional shift of feeling relieved or grateful. Using synonyms can help to vary your writing and create more descriptive narratives that evoke emotion and communicate the scene more accurately.