There are several synonyms that can be used instead of "gain the ascendancy". One alternative is to use the phrase "take control", which means to gain the power or authority to direct a situation or decision. Another option is to say "seize the upper hand", which indicates taking advantage and gaining an advantage over a situation or opponent. "Achieve dominance" is also another phrase that can be used and suggests having the ability to control and govern a situation. Lastly, "establish superiority" is another synonym that means to gain the upper hand over someone or something, indicating that you have more authority or power than others.