We used to do events back when J and Cult were the largest clans around, that were sorta RP-based (not really though).
We'd do 3-5 map clan battles. Each side would have a "headquarter" map. The first battle would be in the middle map, if J won the next battle would be closer to the Cult Headquarter map (so if it was a 5 map event. The first battle would be on map 3, if J won the next would be map 4, if Cult won the next would be map 2. Map 1 would be the J Headquarters, Map 5 would be Cult).
Once one side captured the other sides headquarter the event would be over with the winning side "controlling all the planets".
There was somewhat of an RP element to it, but it wasn't really done for RP. It was more for the sake of ego (who's the best duelling clan. Unsuprisingly J beat us far more than we beat them). But it was good fun.
We also had locked event servers for our clans and would use spies to find out the passwords of the opposing clans servers and do a 10-15 man raid everytime they had an event (usually near the end of the event, so to let them do whatever they had planned first). It was all in good faith though. Me, SK and Aaron remained friendly, same with all the members of our clans. When we tried to do the same with tryhards like in TIN though they weren't so willing to play along.
I'm sure you could recreate something like that but more fleshed out, if you could find the people for it.
Edit:
As for the clans themselves we incorporated RP stuff into the ranks. J's ranks were Y (Youngling), P (Padawan), K (Knight), M (Master), C (Council). I wouldn't call it entirely RP centered but there was some stuff that aligned with lore such as Knights taking Padawans and training them to pass their trials. Cult was the same but with more ranks and branches (different trials for Open Saberists, Duel, FW and Gunner players). We had promotion and recruitment ceremonies, you were expected to swear an Oath to Marka Ragnos and his Prophets etc...
The RP was, however, not the main focus of either clan. I'd say Cult was more deep in RP than J was but both were mostly just focused on being the best dueling clan, with whatever RP being done just being a secondary thing for fun.