It depends on which leadership theory you want to base your research on. And it depends on what instruments you have access to.

For the teacher leadership styles: Style approach, situational approach

For the personality profiles: big five and trait approach ( can be changed or modified and added)

There is no one best instrument to measure and estimate teachers' leadership styles, as different instruments may be more appropriate for different research questions and contexts. However, there are several self-reported questionnaires that have been developed to measure leadership styles in general, which can be adapted for use in the education context. One example is the Authentic Leadership Questionnaire (ALQ), which measures four dimensions of authentic leadership: self-awareness, relational transparency, internalized moral perspective, and balanced processing. Another resource for measuring leadership styles is the Leadership Instruments Library (LIL), which reviews over 100 measurement tools that provide individual and organizational measures of leadership across all types of leadership, including educational leadership. Ultimately, the choice of instrument will depend on the specific research question and the context in which it is being used.