There are several synonyms for the phrase "hove a sigh of relief" that can be used to convey a similar sense of relief and relaxation. These include "exhaled a sigh of relief," "let out a sigh of relief," "breathed a sigh of relief," and "sighed with relief." Other options include phrases such as "relaxed," "unwound," "calmed down," "settled down," and "eased up." These synonyms can be useful for writers and speakers who wish to convey an atmosphere of relaxation and calm, particularly in situations where stress and tension have been alleviated.