As far as I know, no lore has been released about the Order of the Aster in 5th Edition ...
I did search a lot of Wikis and all source books that I have access to (I don't have the modules, so I can't say if it is mentionnedmentioned in Dungeon of the Mad MageWaterdeep: Dungeon of the Mad Mage or Dragon heist Waterdeep: Dragon Heist adventures...) and I was unable to find anything post 1390 DR concerning the Order of the Aster.
I did go through the list of all "famous" members of the Order on all wikis that had one ... I'm thinking this specific Order has not been mentionnedmentioned in 5e. But that certainly does not mean the Order does not exist anymore.