I know a lot of people have talked about this, but here are my 2 cents:
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Predator VS Predator (New training grounds map, same maps from multiplayer, basically a quick multiple round game mode for Predator players to get better; beat a player in 3 rounds to win)
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Bad Blood (One Predator must escape to their mothership while completing objectives, while another Predator hunts the Bad Blood Predator)
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Fireteam VS Fireteam (One squad must find and retrieve a Predator corpse in any map before the other one to win, just like in a normal game when a squad kills a Predator and waits for evac, but the body is randomly hidden, and another way to win is also by eliminating the other team first)
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Single Pred Deathmatch 1v1-4v1 (Firesquad VS one Predator, 5 minute time limit, multiple respawns)
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Deathmatch 2v2-5v5 (Firesquad VS Predators that only have ranged weapons, for fairness, in a 5 minute, multiple respawn game)
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Predator Deathmatch 2v2-5v5 (Predators VS Predators with all weapons, evenly match, 5 minute limit, multiple respawns)
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King of the Hill (5 Predators battle for dominance of a randomly placed area, no respawns, 3 rounds)
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Search and Destroy (Up to 4 Firesquad members try to locate a self destructing Predator within a 5 minute time limit, randomly in a map, with AI enemies about, and try to defuse the bomb through the minigame)
Just a few ideas for now, though there are many more.

