It's possible to add new animations to the character models, but getting the characters to then perform them is more of a problem.
Adding the animations involves editing the model to do the animation frame-by-frame, and so is laborious and time-consuiming in the extreme.
Getting the animation to run in-game is more of a problem. So far, aside from animations which always run (like the flowing cape, which required, as far as I know, editing every
animation for the Revan model so it moves in all situations), it's been done by replacing existing animations (i.e., the "leaning" animation that was originally going to go into the TSLRP).
The problem for animations conversations/cutscenes and their scripting is that as far as I know, the animations which can be used in dialogues/cutscenes are pre-set by the engine and listed in nwscript.nss, and animations for use in scenes have to be drawn from this list, so adding new ones isn't really possible unless you replace some of the existing ones.
There are a few threads on the subject about, but because it's difficult and time-consuming, it's not really that well-documented as a subject:
Animation Fixes tutorial by Imptacular
Switching Model Animations tutorail by Ӄhrizby
Hunter's Run's WIP thread
So far as I know, these are the major threads on the topic. I'd suggest taking a look at these. It's not really my specialism, though, so take what I tell you with a pinch of salt.