Who's to say Leia can't be some kind of field agent for the New Republic in its early years? While Mon Mothma works to stabilize the new government from its core, Leia could be off visiting various worlds trying to bring them to the New Republic - almost like what we see Count Dooku do in the Clone Wars series. There's nothing to prevent her from training during these adventures. Once Mon Mothma has retired, Leia could take over her position. By this point her training would've been over a long time ago. The biggest mistake the EU made was having Leia become Chief of State in her early 30s (and neglected to a supporting role while Luke and Han were still center of attention) then deciding to become a badass Jedi going off on adventures in her 60s (when at this point the next generation should have been taking over). It makes more sense for the two roles to be switched the other way around.