The best way of describing your strategic thinking skills in a management-level job application is to give clear examples of situations in which you have applied those skills. These examples should be as recent as possible, though if you have a particularly good older example, you could include it among several others.
Assuming that you have not been given other specific parameters for the application, your examples can be quite short, and there should be several of them. In each case, state your goal, your strategy for achieving it, and how you planned for contingencies. You might also add anything you would have done differently if you faced the same challenge today. This shows how your strategic thinking has developed, but is best applied to the oldest example you select.
Attached below is a brief article from the Harvard Business Review on how to demonstrate your strategic thinking skills. The author emphasizes the importance of clarity, showing where you stand on any issue and what you would bring to the table when tackling it. You might consider following your examples with a case study in which you bring your strategic approach to an area of business close to that of your potential employer.