The phrase "assert greater authority over" is correct and usable in written English.
It can be used in contexts where someone is claiming or exercising more power or control over someone or something.
Example: "The new policy allows the management to assert greater authority over employee conduct and performance."
Alternatives: "exercise more control over" or "claim more power over".
Some Iranian hard-liners are said to believe that such a war would benefit them, allowing them to close ranks and assert greater authority for the elite Revolutionary Guards.
Above all, we sense a growing desire among voters around the world for leaders to assert greater authority and deliver deeds rather than process, results rather than abstractions.
It was perpetuated in part by European politics, as rival rulers supported either the pope in Rome or the pope in Avignon to assert ever greater authority over the church in their realms.
Mr. Peters has said that he was acting within his authority to assert greater control over the schools' investigations office.
A New York Times video follows the challenges faced by Ms. de Jesus and other residents of Complexo do Alemão as they grapple with the resurgence of violence following an effort by the authorities to assert greater control over big swaths of Rio.
Both the cabinet and the Chamber were determined to assert greater control over the war effort, so that the high command's authority was steadily whittled away.
They are also learning that in the new Mexico, under President Vicente Fox -- a former soft drink executive -- there is a new authority that must be dealt with: an independent-minded Congress that is trying to assert greater power over the nation's agenda.
Despite criticism from contemporaries and historians, many of whom disagreed with his policies and found his leadership wanting, McKinley was a President who acted decisively in going to war with Spain, asserted great presidential authority over his cabinet and generals, and understood the link between foreign markets and national prosperity.
So far Ecuador's armed forces, arbiters in the ouster of three presidents in the last 11 years, have bent to the will of Mr. Correa, a widely popular left-leaning president who has sought to assert greater state control over Ecuador's petroleum and mining industries while challenging the authority of political institutions like the country's Congress.
