Regency
A regency arises when royal authority is exercised by someone other than the reigning king — either because no king is on the throne, or because the king is alive but unable to govern. Two short notices in the historical books describe such arrangements.
Edom Without a King
The notice on Jehoshaphat's reign records that Judah's neighbor to the south is governed by a stand-in: "And there was no king in Edom: a deputy was king" (1 Ki 22:47). The line tells the reader why Edom can be commanded from Jerusalem — there is no Edomite throne to negotiate with, only a deputy holding the place.
Jotham Over the Household
The other case is internal to Judah. When Yahweh struck Azariah with leprosy, the king continued to live but withdrew from public life: "And Yahweh struck the king, so that he was a leper to the day of his death, and dwelt in a separate house. And Jotham the king's son was over the household, judging the people of the land" (2 Ki 15:5). Jotham administers and judges in his father's name while Azariah remains the king "to the day of his death." The crown does not pass; the function does. The arrangement runs until the older king dies.