The phrase "at a new assignment" is correct and usable in written English.
It can be used when referring to a specific task or role that someone is starting or has recently started.
Example: "She was excited to begin her work at a new assignment in the marketing department."
Alternatives: "in a new role" or "on a new project".
Federated Department Stores, Cincinnati, has begun a review for an agency to create campaigns for Macy's aimed at Hispanic shoppers, a new assignment for much of the country.
U.S. officials said that Roger is expected to remain at the CIA in a new assignment which has yet to be determined and that he is being replaced by an agency veteran who has held a series of high-level positions, including running the CIA's operations in Afghanistan.
Pulled back from Amsterdam, where he has "been getting baked/Just looking up at birds" he gets a new assignment from his spook boss and father (Terry O'Quinn) to move some money around in order to short-circuit Iran's nuclear program; things go wrong fast.
In 2008, Flynn got a new assignment, at the Pentagon, as the senior intelligence officer reporting to the Joint Chiefs of Staff.
Sergeant Betancourt married his wife, Nadine, on Dec. 30 and on Jan . 5reported to a new assignment at Fort Stewart.
After 30 years as a copywriter and creative director in various advertising agencies and companies, Shlomo Gewirtz of Manhattan found himself in a new assignment at an Internet telephony company.
"Mr. Secretary," the soldier asked, "how will sequestration affect military P.C.S. movements?" The initials P.C.S. are military shorthand for "permanent change of station," the official term for being given a new assignment at a new location as members of the military advance their careers.
For Schloesser, who was already preparing to leave for a new assignment at the Pentagon, a decade of planning and carrying out a secretive counterterrorism campaign against Al Qaeda was just beginning.
Anticipating a new assignment at the bureau that would force his family to move out of the Newark area, he left the FBI in 1959 to work as a salesman in the precious-metals industry.
