She vowed to 'avenge herself' [=to get revenge], saying she would make him pay for what he had done to her.
The team is out to 'avenge' last week's defeat. [=to defeat the team that they were defeated by last week]
They vowed to 'avenge' their father by capturing and punishing his killer.
(..) Come in. Sit down. A couple hours ago, I had the opportunity to stop Reddington. He was ready to... take one life to avenge another, and in the end, I... I was gonna let him do it. I actually wanted him to do it. Thank God Kirk wasn't in that car. Well, now we know why. (..)2016 TvShow: The Blacklist Title: Alexander Kirk (No. 14): Conclusion Season: 3 Episode 23
(..) to see the inside of that hearing room. I'm gonna kill him the instant he steps out of his vehicle. You and I both know... nothing less will protect Agnes and avenge Elizabeth's death. Red... how come... Harold, you and your people... I will always be more grateful than I could ever express, (..)2016 TvShow: The Blacklist Title: Alexander Kirk (No. 14): Conclusion Season: 3 Episode 23