You may want to check out Ebon Flame.
They have been around since the earliest days of Moonglade and still seem to be going strong. I don’t know how much RP they do as I don’t believe that I have interacted with anyone in the guild for over a decade, but there are still members with an interest in RP.
There may be some other Alliance guilds that are similar, but I spend most of my time adventuring so I rarely see recruitment announcements or social gatherings (and apologies to anyone that I’ve absentmindedly ran through without thinking). There are some socially active guilds in the Horde too, but again, I’m unsure how many are into both PVE and RP.