Your answer was task / process oriented. (It was something on the lines of preparing a hands-off PMO of your own project). But that was not what was being asked. The question was about leadership.
Leadership is about enabing others (to perform at their full potential) in order to achieve a desired result. Notice what I underlined: “Enabling others” + “Desired result”.
So your answer should discuss how you enable others to perform at full potential: playing their strengths, helping them /backing them up on their weaknesses, minimizing conflict, creating a positive working environment, making sure they don't spend much time on dead-end analysis, ensuring good communication within the team and with its stakeholders (manager, partner, client), you give constant training on the job and meaninful feedback, you keep them motivated and excited, etc.
To be honest, what I described is in a sense a manager role - the senior consultant role is to support the manager in doing this. That is why a lot of times it is described as being an associate (associate manager). They support the manager either by doing it him/herself, or by intermediating the relationship between the analysts and the manager, or even by giving a positive example.
Of course, one has to make sure that all the “enablement” it is oriented towards project success, i.e., this is not (just) about making sure everyone grows and gets along. It is doing so in the context of pursuing a specific goal. So focusing the team on the right priorities, making sure deadlines are met (or at least well managed), etc., is paramount.