Previous work has demonstrated remarkably reproducible and consistent hierarchies of neural timescales across cortical areas at rest. The question arises how such stable hierarchies give rise to adaptive behavior that requires flexible adjustment of temporal coding and integration demands. Potentially, this previously found lack of variability in the hierarchical organization of neural timescales could be a reflection of the structure of the laboratory contexts in which they were measured. Indeed, computational work demonstrates the existence of multiple temporal hierarchies within the same anatomical network when the input structure is altered. We posit that unconstrained behavioral environments where relatively little temporal demands are imposed from the experimenter are an ideal test bed to address the question of whether the hierarchical organization and the magnitude of neural timescales reflect ongoing behavioral demands. To tackle this question, we measured timescales of local field potential activity while rhesus macaques were foraging freely in a large open space. We find a hierarchy of neural timescales that is unique to this foraging environment. Importantly, although the magnitude of neural timescales generally expanded with task engagement, the brain areas' relative position in the hierarchy was stable across the recording sessions. Notably, the magnitude of neural timescales monotonically expanded with task engagement across a relatively long temporal scale spanning the duration of the recording session. Over shorter temporal scales, the magnitude of neural timescales changed dynamically around foraging events. Moreover, the change in the magnitude of neural timescales contained functionally relevant information, differentiating between seemingly similar events in terms of motor demands and associated reward. That is, the patterns of change were associated with the cognitive and behavioral meaning of these events. Finally, we demonstrated that brain areas were differentially affected by these behavioral demands - i.e., the expansion of neural timescales was not the same across all areas. Together, these results demonstrate that the observed hierarchy of neural timescales is context-dependent and that changes in the magnitude of neural timescales are closely related to overall task engagement and behavioral demands.