I vaguely remember reading a science fiction story in which the character was introduced as a unambitious government official (a bureaucrat). I believe in the story it mentions that while his superiors had come and gone, he always remained due to his unoffensive nature. Throughout the story the character manipulates his way to meet his ends (which I believe had something to do with aliens and their rights). I believe it was written by Asimov, but it might have been Arthur C. Clarke or Robert A. Heinlein.
It's Asimov's 'Blind Alley'. It wasn't so much people had come and gone as he had played multiple parties to his end.
In the universe of the Galactic Empire (which would include eventually the Foundations), a non-human race is discovered and carefully herded to a planet to use as a combination zoo, laboratory, and reservation. Desperately unhappy, they are dying off, until the administrator in charge of their cage launches a clever plan to buy them escape and freedom. [Blurb from Jenkins' Guide]
Possibly The Star Beast by Heinlein. A major character is Mr. Kiku, a bureaucrat whose actions drive much of the plot. He is a civil service man who watches political appointees come and go. He is not the major protagonist however.
The major plot is driven by powerful aliens who are attempting to regain a member of their species who was 'kidnapped' as an infant; it may be the protagonist's pet.