Left silk radical — the indexing component. The image is of a thread winding round and round something, the literal action 绕 names. 纟 puts 绕 alongside other binding/winding words: 缠 (wind around), 织 (weave), 结 (knot), 绳 (rope).
Right 尧 supplies the sound (yáo → rào, y/r drift). Phonetic family: 烧 (burn), 浇 (pour), 晓 (dawn), 饶 (forgive) — all keeping yáo/ráo/shāo readings tied to this right side. Pure phonetic role; no semantic carry-over from 尧's lofty meaning.