In the context of the future urban mobility airspaces, U-space lays the foundation for unmanned aircrafts to be integrated with conventionally manned traffic to offer a multitude of services to citizens and businesses, such as urban public transport, goods movement, parcel delivery, etc. Given these extensive possibilities, it is estimated that thousands of aircrafts (or even more) from different owners will share common airspace volumes, and the probability that all of them will travel without colliding is extremely low if no means are put in place to prevent it. This paper aims to introduce the reader to the conflict management policy proposed in U-space and proposes a new version of the PCAN (Prediction-based Conflict-free Adaptive Navigation) algorithm to adapt to this policy. In particular, the new implementation of PCAN takes into account a more than likely classification of flights according to their priority. The evaluation of this priority-aware algorithm shows that it is still possible to avoid any conflict between the set of aircraft in flight, with an insignificant detriment to higher priority flights, while maintaining minimal detriment on average.