raise, plan, project, behavior, actions
擧 centers on lifting something up, both physically and figuratively: raising an object, putting forward a plan or project, and by extension the actions or behavior one puts forth.
擧 is the traditional form of 挙. It combines 與 (which likely contributes the sound) with 手 (hand) at the bottom, suggesting raising with the hands. The modern simplified form 挙 replaces the upper part with a simpler shape.
The top component 與 looks like a pair of hands lifting something, and the bottom 手 is a hand. Together they show many hands raising something up, like a project or a plan being put into action.
For キョ, imagine a key (キー) being raised up to unlock a new plan: key -> キョ, and the hand lifts the key to start the project.