There are some new art-oriented platforms that have come into existence lately that seem to be getting a lot of attention, but I don't anticipate they will gain the same popularity that the current giants. Neither uses the same type of algorithm that most social media platforms employ, as both seem to downplay the "popularity = reach" paradigm.
Artfol is growing rapidly, but I think it has an emphasis on its internal community more than anything else. I don't see many people on there using the app to connect with non-artist followers, so it's more like ArtStation or Behance or DeviantArt than Instagram, in my opinion. There's a lot of anime and manga on there, and from what I've seen the user base seems to skew toward a younger crowd of teens and young adults. At least in my opinion. It has optional challenges, a community message hub, a method for asking for critique, and it limits the number of hashtags and categories one can use when uploading your work.
Bubblehouse has some very very cool design features for display, and seems to have a LOT of non-artist users. It's only iOS right now, but will be getting to Android soon. There's more of a variety of art including photography, comics, and animation Bubblehouse. The app still crashes at times for me, personally, and there are a lot of "placeholder" accounts with one or two images, but it's the closest "replacement" I've found to Instagram. It's very slick, but currently has a very small user base.
Anyway, thought I'd share the two alternatives that have wafted into my life currently. I doubt they'll ever reach the levels of popularity that our current slate of social media platforms has, but they're interesting to explore.