"a new balance" is correct and usable in written English
You can use this phrase in several ways. For example, "I'm looking for a new balance between work and leisure."
Opening Day 1904 suggested a new balance of power, with New York's Jack Chesbro beating Boston's Cy Young, 8-2.
Ideally for both countries, China's efforts would create a new balance of power in the region.
We had to find a new balance between defending and attacking but now we are stabilised".
But a new balance of power, not all that different from the previous one, is emerging.
Now, a democratic Chile is searching for a new balance between development and the environment.
The need to strike a new balance is urgent, said Mr. McGregor of APCO Worldwide.
But the Democrats said that the commission had struck a new balance favoring the largest corporations.
The ongoing global economic and environmental crisis presents the opportunity to strike a new balance.
For the law firms, the pay increases also reflect a new balance of geographic power.
The fact that there is a new balance of power adds a degree of confidence.
So they are likely to become far more prevalent as Americans accept a new balance between security and privacy.
