spur a horse on, expel, drive away
驅 centers on forceful movement: urging a horse forward, expelling something, or driving it away. The common thread is causing something to move with energy or pressure.
驅 combines 馬 (horse) with 區, which likely contributes the sound and the idea of driving or urging. The character originally referred to spurring a horse, and later extended to expelling or driving away in general.
A horse 馬 on the left and a complex right side 區 that looks like a whip or a forceful push. Picture a rider spurring a horse to drive it forward, expelling it from a resting state.
For ク, imagine the sound of a whip cracking: 'ku!' as the horse is spurred on. The sharp 'ku' sound cues ク while the horse is driven away.