Jackson Rathbone has been playing the role of Jasper Hale since Twilight (2008). We haven't had scenes that were mainly about him, occasionally seeing him with the other Cullens in the background.
In New Moon, Jasper is one of the reasons for Edward and the Cullens leaving. He attacks Bella at her 18th Birthday Party (held in the Cullen mansion). We get to see hom run to Bella, and then Edward throw him across the room.
But in Eclipse, we get a look at Jasper's history, and him training the CUllens for the fight against the newborn vampires.
Below is an interview taken from
http://www.eclipsemovie.org/ with Jackson and him telling us some things about what we'll see in the upcoming films:
"MTV: Are there training scenes in “Eclipse” along these lines?
Rathbone: It’s interesting; there’s a lot of cool scenes where Jasper trains the Cullen family on how to fight the newborns. He gets to train Emmett — and Emmett is a born fighter — so he’s telling Emmett all these techniques, and Emmett thinks he could just best Jasper [during their sparring]. Jasper ends up getting the best of him, because it’s a war mentality, not just a street brawl. It’s about thinking ahead; it’s a chess game.
MTV: Cool. Will we see the scene where Jasper gets bitten?
Rathbone: Oh yeah, we have to see that. It’s going to be great. I’ve been studying up a lot on the Civil War and that era. It really was a crazy time. It was all-out war on our own turf and between countrymen. That’s terrible. It’s an interesting time to see when Jasper was actually human and what his human form was and, when he gets turned, how intense and how dark he is. Then [we'll see] his realization of what he’s become, him finding Alice and being redeemed by love.
MTV: And is that the first time we’ll see your powers?
Rathbone: Actually, in “New Moon,” we get a little glimpse. Inside the school."
-New Mooner211