Entry 1 sense Webster, 1913 Hagiarchy /(hā"jĭ*är`ky̆)/ · Ha·gi·ar·chy · IPA /ˈheɪdʒiˌɑː(ɹ)ki/ 01 n. A sacred government; government by holy orders of men. 1. A sacred government; government by holy orders of men.