The phrase "an important assignment" is correct and usable in written English.
You can use it when referring to a task or project that holds significant value or priority.
Example: "I have been given an important assignment that requires my full attention and dedication."
Alternatives: "a crucial task" or "a significant project."
If you fail to finish an important assignment, you'll hear about it.
Dr. Bodnar, an adviser to Mr. Dolan, had been given an important assignment last year — settle a patent dispute with the Canadian generic drug maker Apotex.
He wrapped tape around the edges and presented it to his customer like a child who had just completed an important assignment.
This was an important assignment because Miers had spent most of her life in private law practice, serving most notably as the President's personal attorney.
As in all good noir novels, a series of deeper, more paranoid and more personal questions soon arises: Why has the inexperienced Sami been given such an important assignment?
One report in particular, however, in which he erroneously claimed to be standing on "hallowed ground" where American soldiers had been killed by friendly fire, should have given Fox second thoughts about giving him an important assignment in Iraq.
Back on land, Jun Do is promoted to a more important assignment accompanying an intelligence team to Texas.
Somervell met Groves outside the hearing room where Groves had been testifying before a United States Congress committee on military housing and informed him that "The Secretary of War has selected you for a very important assignment, and the President has approved the selection .
For now, though, she has a different — and important — assignment from Attorney General Eric Holder.
And he saw his new job as "a God-sent opportunity" to continue his urban priesthood at the highest levels, and (he was then in his early fifties) to "finish my career in the Church with a tough and important assignment".
