The phrase "has a hold upon" can be replaced with a variety of synonyms depending on the context and tone of the sentence. Some options include "has a grip on," "exerts control over," "holds sway over," "exercises authority over," "dominates," "holds in thrall," and "wields power over." Each of these phrases conveys a sense of one entity having a strong influence or control over another. When choosing a synonym for "has a hold upon," it's important to consider the overall meaning and connotations of the sentence to ensure the most accurate and appropriate word choice.