Effective leaders can balance the conflicting needs of leadership and management.
There is a huge problem with language in this important question. A successful leader/manager must have both leadership and management skills. These are required for effectively regulating the system that the leader is responsible for (whether that system is a team, an organization, a community etc.). The leader's task is to effectively balance the tasks of leadership and management to sustain the viability and prosperity of their organization.
Management is the task of organising complexity. It is focused on maximising efficiency by optimising performance through the elimination of waste. The point of management is to maximise the achievement of the given goal (usually maximise profit) in the current situation. In short, management is about optimising processes to deliver the greatest results today.
Leadership is the task of enabling people to cope with challenging change. It is focused on maximising adapability and unity by providing the necessary framework for people to adapt. For example, providing a powerful vision that enables heursitic behaviour (vs. the algorithmic behaviour of management), clarifying values etc. The point of leadership is to enable the organization to cope with the changing world; leadership therefore is inherently focused on the future and possibilities whereas management is focused on the present. Without leadership, organisations crumble in the face of change.
The reason why so many leaders and organisations struggle in the 21st Century is that they wrongly believe that management is leadership. A real 21st Century leader recognises the fundamental trade-offs between leadership and management. You CANNOT maximise efficiency and adaptability because the quest for efficiency always eliminates the redundancy and preparations for unknown future events that is crucial for adaptability.
In conclusion, the real 21st Century leader can effectively balance the conflicting demands of leadership and management. However, since the vast majority of education programs are focused on management, the result is that most 'managers' are not aware of the need for this balancing act and, more importantly, lack the tools and capabilities to perform this balancing act effectively in a complex, uncertain and volatile world.