The phrase "holds sway over" means to have power or control over something or someone. The opposite of this could be "lacks influence over," which means to have no control or impact on a situation or person. Another antonym could be "yields to," which implies giving in or submitting to the will of someone else. Alternatively, "shares power with" could also be an antonym, suggesting a more collaborative or democratic approach to decision-making. Finally, "loses grip on" could be used as an antonym, conveying a loss of influence or control over a situation or individual.