'deserve priority' is correct and usable in written English.
You can use it when you want to express the idea that something or someone should receive a certain level of importance. For example: "We should ensure that all members of the community are given the resources and support they deserve priority."
Doctors are forced to argue with one another whose patients deserve priority.
It concludes that these linkages "deserve priority consideration in national development" across Africa.
They deserve priority protection from harms that can have lifelong consequences.
Latecomers don't deserve priority I've campaigned for a long time against rip-off booking fees and other charges at theatres.
These children, when they turn 18, deserve priority in any government program intended to help young people get a start in adult life.
I am not in the habit of covering award exhibitions or art prizes, believing that scholarly endeavors and more focused displays of artwork by living artists deserve priority.
But it has begun sending questionnaires to some groups, and Mr. Owens's complaint deserves priority attention.
❦ Darwin had delved far deeper over many years and certainly deserved priority.
He also threatened for a time to boycott the first scheduled debate, which was set to take place on September 26, claiming that action on the economy deserved priority.
Though cities like Zintan and Misurata deserved "priority in reconstruction" and recognition by history, he said, "fighting and struggle is not a measure for representation in government".
In foreign-policy journals, students of America's role have long argued about which deserves priority: our ideals or our interests — the desire to share the freedoms we have or the obligation to protect our security and husband our resources.
