Walk/run radical wrapping the lower-left — the indexing radical. Pictures a person striding with one foot forward, originally meaning 'to run'. Sets 趋 in the motion family with 起 to rise, 赶 to chase, 越 to surpass. Here the running sense fits the meaning of hastening toward something.
Right 刍 carries the sound, with the regular chú → qū shift in the q-/ch- palatalization series. The fodder sense plays no part; 刍 is purely a sound peg here. Same phonetic shows up in 雏 chick and 皱 wrinkle, both unrelated in meaning.
