What I love about Tumblr is that anyone can get their shit noticed as long as they post at a good time, with the right hashtags, and about a decent subject. And of course good content helps.
One thing I highly recommend is finding popular rebloggers/reposters, going to their blog and adding /submit to the end of their URL. If they accept submissions you'll be taken to their submit page even if it's not listed on their blog (many have shitty themes that hide it). Submit your stuff to as many blogs as possible, but make sure it actually fits in with the things they usually post.
I had pieces reposted by blogs like Eat Sleep Draw, Fuck Yeah Moleskines, Fuck Yeah Watercolor, and others by doing this, which always resulted in a bunch of notes and new followers.
I did something similar recently, I made a drawing/gif inspired by a really big artist whose work I was browsing. I tagged her in my post saying she inspired it, figured hey maybe she'll see it and like it.
The post itself gained traction pretty quickly and got over 400 notes within a few hours. Then I messaged some dude who posted similar stuff and said "hey I made this thing, thought it might fit in your blog". Two hours later they reblogged it, sending an extra 500 or so notes my way. A few hours later the artist I originally tagged ALSO reblogged it, which got me another 1200 something notes and a whole bunch of followers (plus she followed me too, which was neat).
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Draw fanart of upcoming movies and games. Join a fandom before it's oversaturated. I'm at 35k followers because I drew fanart of games like Overwatch before they exploded. or just pick the latest meme image and redraw it (bonus points if you can sneak in a clever reference) Those posts go viral very fast.
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I've found that drawing fanart of specific artists' OCs or middling fandoms, as opposed to fanart of hugely popular stuff, has gained me more followers in the long run. I've also gained followers when I do a sequence of similarly-themed images, or one of those month-long drawing challenges that pop up from time to time. ------