Career blocked by insecure managers

How to get past less experienced managers who are insecure and cares more about protecting their own position than solving problems when making hiring decisions? I have been interested in joining an organisation and waiting for the right time and right role to apply as it was undergoing multiple regulatory breaches and the direction was not clear, until recently the senior executive of the function has been replaced, which is a strong signal that it has reached the bottom and will be revamped. While the organisation is still in a mess, but the situation is temporary and will be improved. My profile is a strong match for the industry, business model and the particular needs of the organisation, except may not be a match for the hiring manager as our experience level is too close and in some areas I am more advanced, which I can identify in the interview. The company's talent team identifies me as a strong candidate and advises me to reach out directly if I see any other role of interest. I tend to have more success meeting senior executives before mid-senior management.