There won't be an official DOA6 tournament... at least not by DOATEC's standards. I predict something much darker is going to happen, and it'll be about more than just winning, but about survival... a literal spin on the tournament's namesake.
1) Phase 4 is still out there. Who knows what random people she may kill?
2) If Raidou's "resurrection" in DOA5LR is anything to go by, Victor Donovan is playing for keeps and will focus on going after the ninjas directly.
3) Christie's fed up with Donovan's abuse of her services in MIST, and there's an old saying that women are unpredictable when they're angry. Out of spite, she might indirectly help DOATEC by handing out confidential documents to a few characters who have been underused in the main plot, serving as motivators to get them more directly involved. The characters in question? Leon (possibly for info implying Rolande's death could've been avoided), Jann Lee (possibly for info on his real parents), and Tina Armstrong (to reveal her best friend's other part-time job).
4) If this doesn't happen in Ninja Gaiden 4, Nyotengu could be repurposed as a victim possessed by Bankotsubo's spirit upon leaving her realm without the permission of her royal family, leading to the restoration of his original body. To do this, Nyotengu first needed to find Gen Fu, who still had physical remnants of Bankotsubo (particularly his nose). Then she has to infiltrate DOATEC and repurpose the cloning technology to recreate Bankotsubo.
5) Bankotsubo becomes way more powerful than before, unleashing a powerful curse that engulfs the world, and rendering Nyotengu to a puppet state. To make things worse, Raidou turns on Victor Donovan and seemingly kills him, supporting Bankotsubo's meaninglessly murderous cause. For his amusement (and for vengeance), he forces those involved in the previous DOA tournaments to meet him at a designated area, or people will die. Here, the focus won't be on winning. It'll be surviving Bankotsubo's wrath.
Meh, maybe my theory's overdramatic and too ambitious. None of this is gonna happen, who am I kidding?