The interviewer is trying to learn more about your level of comfort and confidence with a leadership role. Remember, interviewers want to see you be successful! Your answer will show them where you may need extra support or training, if hired.
Be transparent with the interviewer about what aspect of the role you see as a challenge; however, you must avoid talking yourself our of the role. For instance; if you are to lead a group of 50 people in this position, avoid saying that the biggest challenge will be in leading a large team. Keep your answer positive and provide a solution to the challenge.
"I believe that the biggest leadership challenge in this role will be taking on the task of getting to know each team member on an individual basis. This will be a time consuming task but I am looking forward to it! I like to be engaged in the lives of my team because I feel that it creates more productive employees."
"The toughest challenge when taking on a new leadership role is to fully understand the dynamics of the team. You want to make a great first impression while still being effective right off the bat. It's a fine balance!"
"The biggest challenge that I see from the outside will be to gain the trust of the group. From what I understand, many of these team members have worked here for a very long time and have excellent seniority. I am preparing for a lot of 'how it used to be' comments."
Sales answer example
"Honestly, the largest challenge I foresee is the perception of me being their boss. I often am younger than those that I end up managing, and I am a woman, so that can be quite off putting for some, at least in theory. This wouldn't be the first time I've faced and overcome this same challenge, so I am not worried. I will make a point to not only prove my credentials on paper and in practice, but also once I get to know the team, I see these fears and objections melt away quite quickly."
Marketing answer example
"I think fitting into a team and having them see you as a leader and legitimate contributor is always the biggest challenge in a new role. There is almost always some resistance to change, even if they feel it was needed, because it may not be what they thought it should be, or they thought there should be a different leader in the position. Earning their respect and a degree of being liked is always a challenge, but a really satisfying hurdle, once overcome."