I think Borg might make an appearance in the third film, them being in the five year mission and so on
How about that Enterprise would encounter a Klingon vessel during their voyage, that is under attack by the Borg.
Kirk and company saves them but they are not happy to see the Starfleet people, considering how many Klingons got killed in STID.
Spock figures that only way to defeat the Borg is to work together with the Klingons.
This would create some interesting dynamics, tension and explore both the Klingons and the Borg further in this "new" trekverse