After a bit of argument among the Council, it's decided that they can pretty much treat Kina as Mace Windu's Padawan. For all of the obvious reasons, she's not going to have the standard teacher-pupil relationship with him, but he can at least give her some field experience while teaching her about the Force, and especially about lightsabers, which is probably the one field where she still has the most to learn from the Jedi.

So, when Windu's not in Council meetings, he introduces Kina to the beginnings of lightsaber training.