In contexts referring to the religious aspects of the English term avatar, the more common words to use would be 天下り(amakudari) or 神降(kamioroshi).
Etymology
From Englishavatar, ultimately from Sanskritअवतार(ava-tāra, “descent of a deity from a heaven”), a compound of अव(ava, “off, away, down”) and the vṛddhi-stem of the root तरति(tarati, “to cross”).