If you're looking for synonyms for the phrase "with zest," then you might consider using words like "enthusiastically," "vigorously," or "with gusto." Other options to consider could include "with verve," "with fervor," or "with ardor." Each of these terms can help convey the idea of someone being fully engaged, excited, and energetic about something, whether it's a task, a hobby, or simply a general outlook on life. The words you choose will depend on the exact context you are working with, but any of these synonyms can help add life and energy to your writing and help convey a sense of passion to your readers.