If you were to just frame up the current opening above the half wall, you're going to run in to problems with the wall flexing, possibly cracking the drywall.
Therefore, at a minimum, I would put at least a doubled-up stud at the end of the half-wall that runs from the floor to the ceiling. (But first remove drywall and trim from the end and top of the half-wall.) The floor-to-ceiling double stud will resist the flexing. Then you just fill in the opening with a header, footer and studs; hang some drywall; and patch and paint.
However, to do it "right" you would remove the half-wall and just frame in a new wall using traditional building methods.
Personally, I would choose the right way. It's probably not much difference in effort and price and you end up with a more standard finished product.