when "director"is captalized, does it mean "Director of FBI?"
A White House operator connected him with Extension 163, at the end of the swimming pool behind the Virginia mansion. In response to the ring Ethel Kennedy left the men. The operator told her, "The Director is calling." Ethel didn't have to ask which one. In official Washington there were many directors, but only one Director. She said, "The Attorney General is at lunch."

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In this case, it does mean director of the FBI, but like Aleksandra said below, it is capitalized here to show that he was a person of great stature.  J. Edgar Hoover was the long-time director of the FBI from 1924 until his death in 1972.  He was a huge, larger-than-life figure during his time of service.  He was very powerful in both the legal and political arena, especially in the Washington political environment.

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Capitalization is often used to highlight the importance of the word. Should you hear it, there would be certain stress put on the word. So in general capitalized word "director" does not mean he or she is the director of FBI but in this text he or she surely is a significant person.