There are no priorities between traits; each trait can advance as long as its condition is met without interfering with other traits. Cavalry Leader (applying to MOT) and Panzer Leader both require 40% of divisions be of the needed type (see https://hoi4.paradoxwikis.com/Commander_trait#Gainable_traits for conditions). They would both progress simultaneously in your example.2) Let's assume an army made up of 4 MOT divs and 4 ARM divs has a commander and uses both kinds of divisions in equal fashion when attacking / defending. What trait will be prioritised by combat experience of the divisions? Is it tank commander or combined arms or does it get mixed / divided?
Combined Arms Expert is an assignable trait which is not directly affected by combat experience, see https://hoi4.paradoxwikis.com/Commander_trait#Assignable_traits.
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