Semantic cognition is underpinned by ventral anterior temporal lobe (vATL) which encodes knowledge representations and inferior frontal gyrus (IFG), which controls activation of knowledge based on the needs of the current context. This core semantic network has been validated in substantial empirical findings in the past. However, it remains unclear how these core semantic areas dynamically communicate with each other, and with other neural networks, to achieve successful semantic processing. Here, we investigated this question by testing functional connectivity in the core semantic network during semantic tasks and whether these connections were affected by cognitive ageing. Compared to a non-semantic task, semantic tasks increased the connectivity between left and right IFGs, indicating a bilateral semantic control system. Strengthened connectivity was also found between left IFG and left vATL, and this effect was stronger in the young group. At a whole-brain scale, IFG and vATL increased their coupling with multiple-demand regions during semantic tasks, even though these areas were deactivated relative to non-semantic tasks. This suggests that the domain-general executive network contributes to semantic processing. In contrast, IFG and vATL decreased their interaction with default mode network (DMN) areas during semantic tasks, even though these areas were positively activated by the task. This suggests that DMN areas do not contribute to all semantic tasks: their activation may sometimes reflect automatic retrieval of task-irrelevant memories and associations. Taken together, our study characterizes a dynamic connectivity mechanism supporting semantic cognition within and beyond core semantic regions.