At times, an individual might have two University duties that are in conflict because one would create a bias or improper influence upon the good faith execution of the other (e.g. when a Principal Investigator on a research protocol is also a member of the Institutional Review Board).
The general policy on conflicting University duties (linked here) states that, once the conflict is identified, the individual with the conflict must disclose the matter to his or her supervisor (or both supervisors if the different duties are under different supervisors) for resolution. The policy then provides some details and guidance to the supervisor(s) about how to resolve the conflict (e.g. implement an effective management plan or reassign one of the University duties).