I have heard from scholars that If anyone has a problem of involuntary urine discharge he or she can perform each namaz with new wudu each .
What is the ruling on reciting Quran paak in such situation?

Yes before every namaz, wudhu has to be done and the wudhu will become baatil when one urinates voluntarily. You can recite the Qur'an with wudhu which does not become baatil till one does not urinate voluntary