Sorry, I misspoke. He pledges to seek RETRIBUTION, not revenge. A synonym for revenge.
Let's consult Websters, shall we?
retribution
noun
ret·ri·bu·tion ˌre-trə-ˈbyü-shən
1. recompense, reward
2. the dispensing or receiving of reward or punishment especially in the hereafter
3. something given or exacted in recompense, especially : PUNISHMENT
recompense, reward; the dispensing or receiving of reward or punishment especially in the hereafter; something given or exacted in recompense; especially : punishment… See the full definition