Whether democratically elected or not, some people are in power for unusually long. What word distinguishes for example, a democratically elected official who has been in power for 40 years versus one that's been in power for 2 years?
You might think such a word is inappropriate because there's no clear place to draw the line where "unusually long" starts, but in baseball we do have the term "veteran player" to describe a player that has many seasons of experience. In this context "veteran" usually has a positive connotation.
The term "veteran president" or "veteran dictator" doesn't seem right because "veteran" has a positive connotation (meaning "well experienced"), whereas for unusually long or dangerously long terms in office one might want to use a word that puts emphasis not on the benefit of having a lot of experience, but maybe on the drawbacks of being in power for such a long time.