The phrase "a more important problem" is correct and usable in written English.
You can use it when comparing the significance of different issues or challenges, indicating that one problem holds greater importance than another.
Example: "While there are many issues to address, climate change is a more important problem that requires immediate action."
Alternatives: "a greater issue" or "a more pressing concern".
A more important problem is conceptual.
A more important problem is postal voting fraud.
On one hand, those in favor of the drug's illegality are likely to see high rates of use as a more important problem that should be afforded more resources.
A more important problem with the new policy that does depart in a significant way from the earlier policy is that many more organizations are included in the new accommodation.
Second, and more importantly, what Nussbaum describes as the show's ultimate failure of nerve partially reflected a more important problem: The inability to find a clear moral vantage point from which to judge Carrie's choices.
SIR —I usually just wince and read past Lexington's offensive mischaracterizations of the American left, but the claim that "the default position on the left" is that global warming is a more important problem than terrorism and weapons of mass destruction is particularly egregious.
The other view is there any more important problem in capitalist society than who gets capital?
In fact, it may be distracting us from a far more important problem: a looming world oil shortage.
Parshu Kulkarni and his co-founder Dion Lim, had discovered a more important game to play in and a much more important problem to solve than ranking keywords for search engines: Enabling teachers to grow stronger connections between the neurons in their young student's minds.
It would not, however, solve a far more important problem, namely the sluggishness of the country's courts.
A far more important problem should concern the design and management of experiments.
