"Holds dominion" is a phrase that conveys a great deal of power and authority. Synonyms for this phrase might include "rules over," "governs," "reigns," "dominates," "wields power," "controls," or "has mastery over." Each of these phrases suggests a strong, centralized control over a particular domain or area of influence. Depending on the context, other synonyms might also be appropriate, such as "supervises," "manages," "directs," or "presides over." Ultimately, the precise word choice will depend on the nuances of the situation and the connotations that the speaker or writer wishes to convey.