ri ‧ val ‧ ry /ˈraɪv ə lri/ BrE AmE noun ( plural rivalries ) [uncountable and countable]
a situation in which two or more people, teams, or companies are competing for something, especially over a long period of time, and the feeling of competition between them ⇨ competition
rivalry between
There has always been intense rivalry between New Zealand and Australia.
The two players have developed a friendly rivalry.
She had never overcome her feelings of sibling rivalry (=rivalry between brothers and sisters) .