When it comes to describing the phrase "hath a hold upon", there are a few different options for synonyms that can be used to convey a similar meaning. Some possible alternatives include "has a grip on," "exerts control over," "has mastery of," "holds sway over," and "commands influence over." All of these synonyms suggest a sense of power and dominance, indicating that one person or entity has a strong hold over another. The particular synonym used may depend on the context and the tone of the writing, but each of these options can help to convey the idea of a firm grasp or control.