The phrase "assert its hegemony" is correct and usable in written English.
It can be used in contexts discussing power dynamics, dominance, or influence, particularly in political, social, or economic discussions.
Example: "The country aimed to assert its hegemony in the region through strategic alliances and military presence."
Alternatives: "establish its dominance" or "claim its supremacy."
Yet with the Minsk process looking distinctly tired, continued prevention (let alone conflict resolution) is not assured.Russia's desire to assert its hegemony in the South Caucasus complicates matters further.
Russia is the most serious obstacle to the American imperialism to assert its hegemony in the Middle East, East Mediterranean, and Eurasia".
The war had not caused any territorial changes, except in the area around Schaffhausen, where the city had succeeded to assert its hegemony over some places that had formerly belonged to the Bishop of Constance.
A climate of retreat had asserted its hegemony over hope.
Urartu became a serious threat to Assyria's northern border as it expanded in a westerly and southwesterly direction, eventually sharing a common border with Phrygia in northern Anatolia and asserting its hegemony over the Luwians.
The party has always sought to assert its legitimacy by representing itself as a bulwark against Japanese hegemony.
For the whole region, the report found the most likely outcome to be what it called an "eroding balance" — essentially, a continuation of the current situation, in which American hegemony is slowly undermined by China's increasing military abilities and growing willingness to assert its interests.
Guantánamo has become a symbol of a rogue American hegemony that disregards the rule of law, even as it uses calls for freedom and democracy as a weapon to assert its influence across the globe.
Congress needs to assert its legislative supremacy.
and the Collective Security Treaty Organization to assert its leadership.
Reebok was swift to assert its support.
