Use this phrase to stress that something is happening with great intensity or passion. She campaigned for social justice with a vengeance.
Pro Tip 2/3
Renewed Force
Apply the phrase when something returns or starts again with much more force or energy than before. The football team lost last week, but they're practicing with a vengeance now.
Pro Tip 3/3
Sudden Increase
'With a vengeance' often suggests a sudden or unexpected increase in the degree of something. The summer heat arrived with a vengeance.