The phrase "a new burden" is correct and usable in written English.
It can be used when referring to an additional responsibility or weight that someone has to carry, either literally or metaphorically.
Example: "After taking on the extra project at work, I felt like I had acquired a new burden that I wasn't prepared for."
Alternatives: "an additional weight" or "a fresh responsibility".
It is unclear how heavy a new burden Mr. Bush might put on Israel.
Now the terrorist attacks, and the fear of more, are adding a new burden on global trade.
So those fees will a new burden at a time when key financial players can least afford them.
"This appears simple, but it's not standard, and it imposes a new burden," said Wang Yong, of the Chinese delegation.
There is also a unilateralist camp that sees a bigger NATO as bringing a new burden of obligations and constraints.
Germany has issued the strongest calls for a new "burden-sharing" agreement, but at this point that would take a long time, both politically and legally, to implement.
"Thus, the court's decision imposes a large, new burden on a majority of the states, including some of the poorest," Justice Scalia said, listing Alabama, Arkansas and Mississippi in that category.
I shoulda aborted your ass!" Even when Precious begins to overcome this abuse through special educational classes – in which she has been enrolled by a sharp-eyed teacher who has spotted her talent for mathematics – and even found a measure of articulacy through burgeoning happiness and self-esteem, she receives news of a terrible new burden of woe in the movie's final act.
After winning the primary by appealing to the party's base with a strong conservative message, Mr. Schundler faced a difficult new burden: showing that he was not too conservative for a broader electorate dominated by moderates.
If the BFI is going to become an official distributor of lottery funds, that will place a whole new burden of financial and legal accountability upon the organisation.
