"To have a conflict" means to be in disagreement or have a negative situation with someone or something, where there is a clash of opinions, interests, or actions. Full definition
I therefore believe I do not have a conflict of interest in relation to the study reported. (sciencemediacentre.org)
And he stressed that whichever district attorneys are involved in the investigation can not have any conflict with the attorney general's office. (observer.com)
Before we can discuss representing you, we must first ensure that we do not have a conflict of interest. (nelligan.ca)