How does one change from the Carolingian empire into the Holy Roman Empire?
If the Carolingian Empire has been formed, it needs to collapse via event before the HRE can be formed. Once that happens, anyone who isn't the former Carolingian emperor can ask the Pope to name him Kaiser of the HRE, assuming they meet the following conditions:
-is Chalcedonian, Catholic, or Fraticelli
-isn't a heretic
-neither Francia nor the Roman Empire exists
-not already an emperor
-has 1,000 Prestige
-has a realm size of at least 180
-is the king of Germany
-is the king of one of the following:
>Lotharingia
>Italy
>Frisia
>Burgundy
-can pay a certain amount of gold, adjusted based on your annual income
The Pope is more likely to accept the request if he likes you (bonus at opinion level 20, 40, 60, 80, and 100), if you're Zealous, if you're a Crusader, and if you have high Piety (bonus at 400, 600, 800, and 1000). He's less likely to accept you if he doesn't like you (penalties at opinion level 0, -20, -40, -60, -80, and -100), if you're a Lunatic and/or Possessed, if you're a Kinslayer, and if you're Cynical.
How the Carolingian Empire collapses via events is as follows: when Crown Authority isn't at least Mid, every time a new Emperor is crowned some vassals may decide to leave the Empire. If the empire shrinks to fewer than 100 Counties, the Empire is dissolved.