The phrase "arch rivals" refers to two people, teams, or groups who have a strong, long-standing competition or rivalry against each other. Full definition
He became an immediate fan favourite after scoring the winner in Arsenal's FA Cup semi-final tie against arch rivals Tottenham Hotspur in his debut season. (theclockend.com)
He even finished 4th once at the expense of arch rivals Liverpool in the 2004 - 2005 season, and has consistently finished in the top 10, which is no mean feat, considering how competitive the Premier League has become these days. (arsenalindiasupporters.com)
A win for sixth place Arsenal can't take them anywhere, but they would move level with arch rivals Tottenham. (thegamblingtimes.com)