The phrase "assert its authority" is correct and usable in written English.
You can use it when discussing the act of demonstrating or exercising power or control, often in a formal or authoritative context.
Example: "The government must assert its authority to maintain order and ensure compliance with the law."
Alternatives: "exercise its power" or "establish its dominance."
After winning back control of Cape Town's city council earlier this year, the DA says that the ANC is refusing to let it assert its authority over the city.In any event, other watchdogs, apart from the DA, are also effective.
Judge Rakoff said the agency settlement policy — "hallowed by history, but not by reason"— creates substantial potential for abuse because "it asks the court to employ its power and assert its authority when it does not know the facts".
She didn't want to see it, didn't want it near her, and when it tried to assert its authority she became afraid of being at home at night.
A referral to the UN security council, if ordered, would represent a show of strength for the court as it struggles to assert its authority.
The new executive is still based in Tunis, however, and only began to assert its authority this past weekend when it called on "all Libyan sovereign and public institutions and the heads of financial bodies to start communicating immediately with the Government of National Accord so as to hand over power in a peaceful and orderly manner".
Hamas may have demonstrated that after several weeks—it has been able to assert its authority over one militant group, but a much more difficult road lies ahead.
The transitional government was formed two years ago but it has been unable to assert its authority over the country.
It was time for the Commons to assert its authority, said Gary Streeter.
Whitehall is keen to continue to assert its authority – and parliament is keen to support it.
Second, it is important for the E.P.A. to assert its authority under the Clean Water Act at a time when both the law and the agency are under fire in Congress.
