"No love lost" is another way of saying that there exists long-standing animosity
When two people, or groups of people, have many, long-standing reasons for disliking one another, then you can say that there is no love lost between them. The phrase is frequently used when describing a rivalry of some sort, for example between two sports teams, who have played against each other in many important games/matches.
Examples:
1. There is no love lost between New York Yankees fans and Boston Red Sox fans.
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