No, leadership is not defined by seniority.
Leadership is the process of guidance, influencing the behaviour of others in order to achieve a goal. Leaders develop their vision and further motivate subordinates to achieve that. It binds a group together and motivate them to achieve their goals. In leadership, a group of two or more people interact with each other and the group's behaviour is being moulded and shaped by an intelligent, mature leader only.
There are many people who talk about a company's leadership referring to the senior executives. Your understanding,intelligence and experience makes you a good leader, and not how senior you are. It is said that people who are senior are more experienced than the young ones. But, there are many who are fighting and are dedicated towards their work and see themselves as a good leader in the near future. Leadership is not that you have when you will reach a specific pay grade, it can happen anytime.
And, leadership has nothing to do with titles. Your title does not define if you can be a leader or not. One can be a leader anywhere, whether it is their family, workplace etc.