The phrase "long-standing rivalry" is perfectly correct and usable in written English.
You can use it to describe any ongoing, extended feud between two persons, organizations, or other entities. For example: The long-standing rivalry between Apple and Samsung has played out in the tech industry for decades.
There is a long-standing rivalry between the Original Six teams, dating back to 1926.
Long-standing rivalry between the Nguyen and the Trinh became open warfare in 1620, with hostilities continuing intermittently until 1673.
Arsenal has a long-standing rivalry with another North London club, Tottenham Hotspur, against whom it plays the "North London derby" match nearly every year.
In 1894 95 the long-standing rivalry between the Japanese and Chinese in Korea led to a war between the two Asian empires, which the Japanese won decisively.
Although Djindjić and Koštunica had united in opposition to Milošević, their long-standing rivalry persisted and soon grew into a struggle for power.
McLaren's and Ferrari's long-standing rivalry is compounded by the Scuderia's special relationship with the FIA – which takes every opportunity it can to punish the British squad.
Long-standing rivalries were put aside as steelmakers were crunched into five main groups.
Three nights a week, chess-players gather at The Café to continue long-standing rivalries.
On a larger scale, this is also what suppressed many long-standing rivalries in eastern Europe during the Cold War.
Even beyond the United Arab Emirates' proposal, the meeting instead laid bare long-standing rivalries and tensions among Arab states.
Murmurs on the sound track introduce the players, whose long-standing rivalries and friendships are taken for granted: We arrive, as we so often do with Altman, in medias res.
