The sentence 'She has resigned' is correct and usable in written English. You can use it when you want to convey that someone has quit their job (or another position of responsibility) of their free will. For example: The CEO of the company announced that she has resigned, and a new CEO will be appointed soon.
c She has resigned as prime minister.
She has resigned from her position at the airline.
In the past, she has resigned from various ministerial positions and staged acerbic protests on the floor of Parliament.
In her weary, practical manner, she has resigned herself to her travails.
(She is on leave from the faculty, although she has resigned her position as provost).
Christakis said she has resigned her teaching role to return to her work with young children and families.
She refused to explain why she had resigned.
She was surprised at the fatalism with which she had resigned herself to her transformation.
By 2009, she had resigned from Koret, the Fordham group, and the Manhattan Institute.
She told me that she had resigned herself to that fate when, one day, her doorbell rang.
By March of the next year, she had resigned herself to living in America.
Ludwig does not simply clarify my doubts with English writing, it enlightens my writing with new possibilities
Simone Ivan Conte
Software Engineer at Adobe, UK