Is there a core set of leadership skills that are essential or mandatory for leadership success?
It's a Yes, and a No
If you read books about leadership, or listen to leadership experts, you may come away with the idea that there are core, mandatory skills and behaviors essential to leading effectively. That's accurate, up to a point.
It's true that most successful leaders will be able to inspire, motivate, create vivid visions, and have credibility and trust on the part of followers, but it's also the case that you can find situations where effective leaders lack one or more of those elements.
The reason is that leadership effectiveness is determined by many interacting factors, and that it is dictated by a combination of leader characteristics, follower characteristics, and situational or contextual factors. What that means, in simplest form is that there are many paths to successful leadership.
So, you'll find that a leader that lacks some of the "required elements" may thrive because the context doesn't require them, or that the leader compensates for the lack of some of the factors by being particularly good at other elements.
This is one of the joys of leadership, and one of its puzzles -- figuring out what works in what situations.
So the answer is that yes, there are probably core characteristics and behavior of leaders, but they are not always requried in any specific situation. There are no universal recipes, and while we can learn from other successful leaders, there's no guarantee that what worked for them will work for us.