It is a little bit odd to speak of a conflict of interest between labor and management because that is not how we usually use the term “conflict of interest.” A conflict of interest usually occurs within one person or one side of a dispute. For example, if a union leader were also married to a member of the company’s management team, both spouses would have conflicts of interest because their connection to their spouses would be in conflict with their duty to the union or the company, respectively. When labor and management come into conflict, it is just conflict, not a conflict of interests.
Let us assume, then, that this question is simply asking how the interests of management and labor can conflict. If this is the case, there are many possible examples. One example would be that labor has an interest in having more people work for the company while management has an interest in reducing costs. Labor would prefer to have more workers at higher wages. Management would prefer to have lower costs by reducing the number of workers. Another example is that labor has an interest in making it harder for the management to fire workers while management has an interest in making it easier. Management wants flexibility but labor wants job security. These are two major and very typical conflicts between the interests of labor and those of management.