Dear researcher, the field of leadership consists of broad and complicate concept. therefore, at first it is better mitigating this issue to a much more specify variable or concept and then base on the way you choose you can search for the questionnaire.
-Shadi Ebrahimi Mehrabani and Noor Azmi Mohamad (2015) New approach to leadershipskills development (developinga model and measure) Journal of Management Development Vol. 34 No. 7, pp. 821-853
Dear colleagues, there is a good book on leadership by Grossman and Valiga (2013). I think it is comprehensive and informative one. It describes leadership skills and how to develop it, in what environment, its mutual relation with followership, in addition to many other related aspects and issues. Also, it includes a number of leadership issues measurements. The reference is: Grossman, S.C. and Valiga, T.M. (2013): The new leadership challenge: creating the future of nursing. 4th ed., Philadelphia: F.A Davis Co.
Another reference, you may find it helpful. It studied leadership abilities and how academic environment could contributes to developing it. Please, follow this link https://www.researchgate.net/publication/317505810_Academic_environment_of_nursing_faculty_staff_and_their_potential_leadership_and_creativity_abilities
Dear researcher I once carried out a research on emotional intelligence (EQ). My subjects were the lecturers of PNG university of technology. I basically tried to measure their emotional intelligence level because I thought there is a direct relationship between both EQ and leadership.
As expected, the results obtained showed strong correlation.
The questionnaire designed were mainly based on EQ. Therefore, I would recommend you search for EQ sample questionnaire.
Leadership is such a broad concept that different models have different definitions, therefore what is expected from a leader varies from model to model.
It would be easier for me to help you if you narrow your research to a specific leadership model. For example, Hershey & Blanchard Situational Leadership Model or Goleman's 6 Leadership styles.
Once there, we could identify leadership competencies (or skills) and create a model to measure their development.
As others have noted, there are many dimensions that could be assessed in multi-rater leadership instruments. I am partial to the ESCI (Korn Ferry) for Emotional Intelligence - a core leadership competency; The Leadership Versatility Index (LVI) form Kaiser Leadership Solutions, which does not use a Likert scale, rather it assess whether the leaders uses too much or two little of behaviors on two dichotomies: Operational vs. Strategic and Forceful vs. Enabling. Finally, the Leadership Agility 360 (from Changewise) addressed stages of leadership development as measured by the level of "agility" that the leaders demonstrates. All of these instruments require certification.