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Yes, you can improve your Leadership skills by setting as a good example to them. Be flexible to the people that surrounds you and influence them by your good Leadership skills within the team so you can work together to turn things for good. To be successful in your career, you must focus more on your goals rather than focus on the people around you that affects your Leadership.
We should encourage the people not as a subordinate but as a colleague. Give him tasks and help him in attaining the tasks.
This is an opportunity to prove that if you are following the organization's principles, processes, and the methods, this will only help you to prove that you are good in what you are doing ( again, if you are being professional and few others recognize it).
Good luck
Yes, there is a greater deal to improve the leadership skills for folks behave unprofessionally, that is what leadership come into picture, if everything is fine then there is not much to improve