The phrase "accepted appointment" is correct and usable in written English.
It can be used in contexts where someone has agreed to take on a role or position, typically in a professional or formal setting.
Example: "After careful consideration, she finally confirmed her accepted appointment as the new director of the organization."
Alternatives: "confirmed position" or "approved role".
In 1964, after Kennedy's assassination, he accepted appointment as head of Pres.
In 1724 he reluctantly accepted appointment as archbishop of Armagh and primate of the Church of Ireland.
After serving as president of the Board of Education (1905 07), he reluctantly accepted appointment as chief secretary for Ireland.
In the winter of 1967, Fisher was ill, but in early 1968 he accepted appointment to the high court.
Despite some misgivings about entering politics, he accepted appointment by the military governor as alderman (1868) and was later (1869) elected to the state senate.
In 1891 Reagan accepted appointment to the Texas Railroad Commission and served as its chairman from 1897 to 1903, when he retired from public life.
While distinguished Canadians have accepted appointments to the Senate, the tendency of governments to use it to reward retired politicians or party operatives has, over time, made it fertile ground for political cartoonists.
Friends and associates like Mr. DeVito; Bill Duke, an actor, director and enrolled Democrat; and Clint Eastwood, a Republican, have accepted appointments to the California Film Commission to try to keep production in the state.
Thereafter, Ramón y Cajal accepted appointments at the universities of Valencia (1883), Barcelona (1887), and Madrid (1892), where he accepted the Chair of Histology.
A year later, Stettinius left private industry to accept appointment as chairman of the War Resources Board.
Jones resigned as RFC chairman in 1939 in order to accept appointment as director of the Federal Loan Agency.
