Nwaka is Ezeulu's nemesis. Every time we see Nwaka in Arrow of God, he's challenging Ulu or criticizing Ulu's high priest, Ezeulu. Nwaka believes strongly that Ezeulu is power-hungry, that he's trying to grab more authority than he is due.
Nwaka appears to be motivated by his friendship with Ezidemili, the priest of a lesser god, Idemili. Ezidemili fortifies and strengthens Nwaka in his attacks on Ezeulu's character. Nwaka might be power hungry himself, or he might be manipulated by Ezidemili, who may be hoping to destroy Ulu so that Idemili can take his place.
Though we don't see any growth in Nwaka's character over the course of the novel, he does accompany the other men when they visit Ezeulu to beg him to announce the day for the Feast for the New Yam. In other words, he squashes whatever enmity he has towards Ezeulu for the good of all of Umuaro.