Alviarin was made Head of the Black Ajah by Ishamael after he removed from the position (and killed) Jarna Malari, the one who had launched a hunt to find and kill the Dragon around the time of Rand's birth.

It's Galina who was replaced on the Supreme Council (and Head of the Red Ajah too, of course) where she stood second to Alviarin. We never learned who replaced Galina on the Supreme Council of 13 women (only Alviarin, Galina and Sheriam have so far been confirmed, and for Sheriam it's confirmed only so far as Verin telling Egwene in her notes Sheriam was one of the leaders).