Swing and shuffle are generally defined as moving the off-beat closer to the end of the measure. What's the reverse of this?
What is it called when the off/up beat is moved closer to the beginning of the measure?
The general term for swing with the short note on the beat is reverse swing.
The Scotch snap is quite common in Scottish music such as Strathspeys, but it is also somewhat popular in hip-hop.
I often use the word "anticipating" when talking about this, e.g. "The Viennese waltz anticipates the 2nd beat slightly, placing it a bit early." In less formal circles I might also call it "pushing" the beat.
Note, I'm looking here for terms that (like swing and shuffle) try to describe a slight offset that doesn't neatly align with a rhythmic value. There's also a phenomenon in many works in which major motion happens earlier than "expected," like chord changes every measure but on the "and of 4" rather than the downbeat, like in this song that I can't get out of my head lately from Matilda: The Musical:
For this phenomenon, I'd definitely use the word "anticipation," e.g. "The chord changes are anticipated by half a beat," as long as it's clear that we're not using the meaning of anticipation related to non-harmonic tones in a melodic line.