Because collective movements have fitness consequences for all participants, group travel can impose conflicts of interest when group-mates vary. Challenges associated with coordinating activities of group-mates, such as during travel, may potentially be mitigated through the use of simple rules governing leadership and other behaviours to minimize conflict. Although individuals living in groups with fission–fusion dynamics may temporarily separate, leadership determination at subsequent reunions, and events occurring during reunions, are poorly understood. Here we investigate leadership during travel prior to reunions of spotted hyaenas, Crocuta crocuta , living in one large social group in the Masai Mara National Reserve, Kenya. Whereas individuals often arrived at dens or joined hunting parties alone, those joining others to participate in group defence of shared resources typically did so when accompanied by group-mates. Although most hyaenas led processions, the attributes of members within each travelling party consistently predicted leadership roles. The highest-ranking adult within each travelling subgroup, often a lactating female, typically assumed the vanguard position prior to reunions. Reunions promoted conflict, particularly at kills. However, as predicted by the conflict mitigation hypothesis, individuals that greeted conspecifics were significantly less likely to fight at reunions than were hyaenas that failed to greet at reunions. Thus, whereas temporary separations may reduce immediate conflicts of interest in fission–fusion societies, hyaenas pay consensus costs at subsequent reunions, particularly in the context of feeding competition, and greetings appear to reduce such costs. Finally, we propose a novel scheme for leadership categorization in which leadership depends on whether or not leadership is based on specific attributes of individual group members. We apply this attribute-based framework to quantify the patterns and mechanisms of leadership during group travel for 52 species of mammals, including the spotted hyaenas studied here, and place findings in a broad evolutionary context. • Individuals may separate to reduce group conflicts, but reunions are poorly understood. • We investigated leadership at reunions in fission–fusion societies of spotted hyaenas. • Leaders at reunions varied, but higher-ranking lactating females led most often. • Reunions promoted conflict, particularly at kills, and greetings mitigated these costs. • Our novel, attribute-based scheme characterizes patterns of leadership across mammals.