You will know that an advertised position is being managed by a consultant/executive search firm if the place for resume submissions is with the firm and not the agency that has advertised the position. If this the case you can call the executive search firm and ask for more details about the position. The firm would have talked to all the stakeholders for the agency including the policy board, the supervisor, employees and other groups that work with the agency. Most executive search firms also post a Profile/Brochure about the position, but it has most of the very positive items and hot topics that are facing the position. But if you want to know the real story about the position, then you should call the executive search firm. They will also be able to tell you if you meet the qualifications before you formally apply for the position. By asking about the details and background first you can put together a cover letter that really addresses the position and even adjust your resume to highlight the most important skills related to the position.
For additional information see Blog about preparing your resume!