Is repeating a year even allowed? Well I did hear that Kiryuin may have a role post graduation from a supposedly trusted source but I don't know how much this information is relevant.
@KingpinRisette in the most likely scenario, no.
Though it may be possible for Kiryuin to do it, I don't really see her staying in ANHS just for Kiyotaka, their relationship from what I have skimmed through the novels, is actually kinda lackluster. Though some of the hardcore Cote fans can give us an actual analysis and theory if Kiryuin might stay in ANHS.
After watching the latest episode of COTE, it's all coming back now as to why I hated Yamauchi a lot. Goddamn, they made him more irritating in the anime than the novel!