Jingū, at Isë, is unique among contemporary jinja, at least as far as I know, in having two chief priests. These are called the Dai Gūji (“Great Chief Priest”) and Shō Gūji (“Small Chief Priest”).
Both of these people are frequently mentioned in Jinja Shinpō, and as far as I can tell, the distinction between them is as follows.
The Shō Gūji is a career priest, and normally someone who has served as a priest at Jingū for years. He (always he) is normally at Jingū, and fills the role played by the chief priest at most jinja.
The Dai Gūji is not a career priest, and spends little time at Jingū. My understanding is that he (again, always he) plays a central role in half a dozen of the most important matsuri every year, but otherwise does not participate in ceremonies.
The Dai Gūji is, however, normally a descendant of the Imperial family, typically from one of the branches of the family that were made into commoners after the end of the war. I am aware of one possible exception, who appears to be descended from the Fujiwara, the noble family that effectively ruled Japan a thousand years ago. (The Tennō has almost never effectively ruled Japan.) However, given the complexities of descent, he may in fact be descended from the Imperial family, possibly with an adoption into the Fujiwara in the background.
This custom does have strong historical roots. First, Jingū is the jinja that enshrines Amaterasu Ōmikami, the Imperial ancestor, and in the Meiji period the highest priest was always an Imperial prince, from one of the cadet branches. Second, in the Edo period and earlier, the highest priest at Jingū was from the Ōnakatomi, another branch of the same clan as the Fujiwara. In both cases, these priests only went to Isë for the most important matsuri.
It also seems to be common for the chairman of Jinja Honchō to be a retired Dai Gūji — the current one is, as was his predecessor. I am not sure whether this is supposed to be a standard succession, in which the current chairman retires when the Dai Gūji retires, so that the new former Dai Gūji can take up the role, but there are no regulations requiring that as far as I recall.
The trigger for this post was a couple of articles in Jinja Shinpō reporting that the previous Dai Gūji had retired, and a new one had been appointed. (There is, as yet, no sign of the chairman of Jinja Honchō resigning.)