In Book 3: Fire, when Azula is not wearing her formal robe in war meetings, she normal wears her royal shoulder and chest Thai armor and an unusual outfit which has both pants and seems to be a weird "tunic" with the middle part slit. For an example, look at where she is hanging on to the cliff with her headpiece.
http://avatar.wikia.com/wiki/File:Azula_hanging_from_a_cliff.png
Can anyone say what her outfit is called?