DYNASTY WARRIORS 9 Empires

There are some story related events that will have someone succeed the current ruler. These are fixed to certain characters and accompanied by cutscenes. It may be possible in other situations, like "Gathering of Heroes", but lets stay in the main story:

Sun Ce will succeed Sun Jian.
Sun Quan will succeed Sun Ce.
Cao Pi will succeed Cao Cao.
Liu Shan will succeed Liu Bei.

It seems to me that you cant just keep selecting "Rest" to force the event. Whenever I tried this, I ended up empty handed. So I would suggest to play the game normally, do tasks, raise your level, get a higher position.

I've had two successful events in the scenario "Three Kingdoms":

Picked Cao Pi - and he succeeded Cao Cao in January 220AD.
Picked Liu Shan - and he succeeded Liu Bei in October 223AD.

Your dates may differ depending on performance. As mentioned above, without any performance you will miss out. I'd personally suggest going with Liu Shan. He's guaranteed to be grand commander in the year 223 if you play the game normally.

It doesn't seem to matter if the position you are offered is Ruler, Magistrate or King, it will unlock on either of them.