[Boromir88]

I don't foresee any wars between Rohan and Gondor, let alone any sort of rifts or tension. At least, not between Eldarion and Eomer, and not in the Fourth Age.

Rohan exists because of Gondor, what I mean is, the lands that would become Rohan was a territory under Gondor's control. When Eorl came to Gondor's aid in the TA 2510, the steward Cirion granted the lands to Eorl and the Rohirrim. Eorl and Cirion made an oath, that in return for Eorl coming to Gondor's aid and promise of lasting friendship that Rohan's enemies would be Gondor's enemies, Cirion granted them Calenardon and their sovereignty.

There's debate that since Cirion was a Steward could Aragorn reclaiming the Kingship of Gondor undo the oath between Cirion and Eorl? Why Aragorn would want to I don't know, but it doesn't matter because he didn't undo the oath. So for one side to break faith with their part of the oath (say King of Rohan siding with Gondor's enemies and taking up arms against Gondor, or the King of Gondor reclaiming the lands of Rohan and absorbing Rohan back into its empire) would be a terrible crime, and probably the worst thing they could do.