The phrase "initiated under" is correct and usable in written English.
You can use it to indicate when a process began. For example: "The project was initiated under the new management team in 2020."
Several projects were initiated under the Sentinel Initiative to augment existing safety monitoring systems.
Any inquiry would be the first initiated under the act by the coalition government.
Programs initiated under Pepfar have shown great success in treating and preventing H.I.V.-AIDS.
44th Parliament opened with a Welcome to Country, a ceremony initiated under Kevin Rudd's leadership.
These programmes were initiated under Ken but then scaled back by Boris and the money channeled into vanity projects.
It was created in 1969 to mimic the five prizes initiated under Alfred Nobel's will.
The dispute stems from an investigation of Hewlett-Packard's directors initiated under the company's former chairwoman, Patricia C. Dunn.
It was initiated under John F Kennedy's Democratic administration and seen through by the Republican Richard Nixon.
After 2008, it becomes harder to separate spending that was initiated under Mr. Bush from that under Mr. Obama.
In 1950 the outbreak of the Korean War initiated, under Soviet pressure, a vast rearmament program in the country.
Shadow business secretary Chuka Umunna said the bank was initiated under the last Labour government to attract funding to projects which would not otherwise receive finance.
