Revenge; getting even with someone (often used colloquially and in sports/drama contexts).
彼は兄の死のためにリベンジを誓った。
He vowed revenge for his brother's death.
その映画は復讐（リベンジ）をテーマにしている。
That movie has revenge as its theme.
あの店の対応が気に入らなくて、リベンジを考えている。
I was upset by that shop's service and am thinking about getting revenge.
Having a second go; a rematch or retry (often used to mean avenging a previous loss in sports or competitions).
前回負けた相手に次の試合でリベンジする。
I'll get my revenge (win back) against the opponent who beat me last time in the next match.
大会敗退の悔しさを胸に、彼女はリベンジを目指して練習を続けた。
Carrying the frustration of losing in the tournament, she kept practicing to achieve a rematch victory.
次はリベンジのチャンスだ。失敗を取り戻そう。
Next is your chance to have a second go. Let's make up for the failure.