I am a consultant who has trained many CEOs and top-level managers from various companies in different countries. One of my specialities is leadership training. Based on my knowledge and experience, I recommend six key areas that contemporary leaders must work on and enhance their skills:

Art of self-discovery: how to understand yourself, leverage your strengths, and be authentic and natural in your leadership. This requires a specific style (using insights from psychology) and proper training.
Emotional intelligence: how to be emotionally aware and competent in dealing with different emotional issues that modern leaders face in their work life. Emotional intelligence can be learned and enhanced.
Evidence-based decision making: how to apply the techniques of problem spotting, problem scoping, problem shepherding, and solution translation to understand and address the challenges posed by the current dynamic world.
Learning the dynamics of a modern globalized world: how to keep up with the changes in the world economy, identify the threats and opportunities in the present and near future, and cope with them effectively. Better risk management is essential for leaders to learn and improve.
Understanding and managing people: how to learn the basics of human society and use the best techniques to motivate and inspire people. Leaders cannot succeed if they do not understand the people they lead in their organizational setting. Modern humans are very complex, and learning the intricacy of human nature is key to leadership success.
Better communication, negotiation, and conflict-resolution skills.
Throughout my career, I have observed that successful leaders are constantly updating their skills in these six key areas, while those lacking leadership skills struggle to comprehend their importance.