"has recently embarked" is correct and usable in written English.
You can use it whenever you want to indicate that someone has recently begun something. For example: My sister has recently embarked on a quest to climb the highest mountains in all of Europe.
But China has recently embarked on a construction spree unprecedented in its scale and speed.
The Union has recently embarked on projects so ambitious that they challenge fundamental assumptions about both politics and economics.
The NYSE has recently embarked on a round of acquisitions and collaborative deals in an effort to become a trend-setter in technology as well as globalisation.
The Kenyan government has recently embarked on the design of an inclusive business ecosystem where government, local pharmaceutical manufacturers and distributors play an active role in healthcare delivery.
The government there has recently embarked on a 10-year plan to improve the quality of its childcare provision by investing in workforce reform.
But the patriarch has presented himself as the country's ethical compass, and has recently embarked on a vocal campaign of public morality, advocating Christian education in public schools and opposing abortion and equal rights for gay people.
The two companies have recently embarked on aggressive marketing campaigns, particularly targeting the vital teenage market.
Diana had recently embarked on a romance with Dodi al-Fayed, and was being hounded by paparazzi eager to get pictures of the couple.
Some will be choreographed by him, some by Kobborg; both men, as well as being good friends, have recently embarked on second careers as choreographers.
I have recently embarked on a level 5 apprenticeship with training provided by DH Associates which I hope to complete within the next eight months.
He had recently embarked on a self-assigned project to research, write and record an album for each of the 50 American states.
