The phrase "priority problem" is correct and usable in written English.
You can use this phrase when referring to a problem that requires urgent attention or needs to be solved before other matters. For example, "Our priority problem right now is to find ways to increase profitability in the company."
Tweets of the Week @larrywinget: You don't have a money problem, you have a priority problem.
However, energy efficiency perhaps remains both the most challenging and highest priority problem due to the scarce energy resources available in sensor nodes.
Through discussions, I have come to know that leprosy is no longer a priority problem and thus funds from our government and international agencies are reducing day by day.
Nowadays contaminated soil has become a major and priority problem, and therefore, during the last four decades many countries have been introducing policies and practices for the management of contaminated soil.
Fundamentally, the reason they are not coming to fruition is a management priority problem, not a technology problem.
Normally when unsecured creditors do so well compared to secured creditors, there's a serious priority problem to investigate.
This is the second of two companion papers proposing priority problems for research on mental disorders.
Chronic pain is one of the priority problems in palliative care.
Stephan, K.E. et al. Charting the landscape of priority problems in psychiatry, part 2: pathogenesis and aetiology.
As you suggest, air travel in the post-9/11 world is unnerving enough without the impromptu antics of pilots who have priority problems.
The Bank report also concluded that most SWAps tried to do too many things, instead of focusing on effectively addressing the priority problems that cause the most illness, disability and death of poor people in poor countries.
