• 帝国ていこく — empire
• 皇帝こうてい — emperor
• 帝王ていおう — supreme ruler; monarch
• 帝室ていしつ — imperial household
• 帝都ていと — imperial capital (old term)
• 帝みかど — archaic word for emperor

With the cloth radical 巾, 帝 suggests a raised imperial seat draped in ceremonial banners. It’s the image of the highest ruler, set apart from ordinary people.