While the first two Legend of Heroes: Trails of Cold Steel games were developed for the PlayStation 3 and PlayStation Vita, the sequel may change things. The PlayStation 4 is ascendant and the gulf between that system and the Vita is much larger than the Vita compared to the PS3. In an interview with Dengeki PlayStation (translated via Gematsu), Nihon Falcom president Toshihiro Kondo admitted that the company was thinking about how to approach Trails of Cold Steel III.
"We plan to start going at full scale this summer, but we've already completed the basic foundation [on Trails of Cold Steel III]. We're also making new models for Rean and company," said Kondo. "However, for those concerned about hardware, there are a lot of PS Vita users when it comes to the Trails series. We're currently considering whether to do a PlayStation 4-exclusive or to make it cross-platform with PS Vita."
Allowing cross-platform with the Vita would likely be the preference of existing Trails players, extending the sense of hardware continuity. It's largely dependent on what Nihon Falcom wants to do with the title and how much they're willing to push Trails III on PlayStation 4. Given today's news, perhaps the Nintendo NX might get some love from Nihon Falcom as a Vita replacement. Who knows?
Legend of Heroes: Trails of Cold Steel III currently has no release date.