The introduction of the porxies (to cure tempering), warding scales (to prevent tempering), teaching the Eorzean beast tribes (and Kojin) proper creation magics to call forth their deities instead of the corrupted summoning arts taught by the Ascians (so they don't want to temper in the first place), and improving relationships with said beast tribes so they're not openly antagonistic anymore (so summons are far less frequent to never) basically tells us they are done with primals as a big antagonistic force.
Given all the souls (aether) that made up Zodiark and Hydaelyn have returned to the Lifestream, it may or may not be possible to call them forth again. It wouldn't be the original / real one though, since the only living person who's seen Zodiark is the PC and the only living people who've seen Hydaelyn are the ex- but not really ex-Scions, none of whom have any intention of doing so. Without an astronomical amount of aether (like, the Mothercrystal's worth) you'd just get a wimpy simulacrum anyway.