Click on the spoiler tags to see the various new additions of move combos for RSE contests. These are basically DPP moves which weren't incorporated since Super Contests took over from DPP onwards. Well, now we finally have DPP move combos to use for RSE contests in the URPG.
A huge thanks to Feng for helping me to consolidate the list.
Spoiler:
Attack Order: Defend Order, Heal Order
Brave Bird: Roost
Charge: Charge Beam, Discharge
Charm: Captivate
Defend Order: Attack Order, Heal Order
Dragon Dance: Dragon Rush
Dragon Rage: Dragon Rush
Dragon Rush: Dragonbreath, Dragon Dance, Dragon Rage, Dragon Rush
Dragonbreath: Dragon Rush
Focus Energy: Close Combat, Drain Punch, Focus Blast, Hammer Arm
Growth: Energy Ball, Power Whip
Heal Bell: Lucky Chant
Heal Order: Attack Order, Defend Order
Leech Seed: Worry Seed
Lucky Chant: Heal Bell
Metal Sound: Metal Burst
Mind Reader: Close Combat
Payback: Assurance, Revenge
Rain Dance: Aqua Jet, Aqua Tail, Brine
Revenge: Assurance, Payback
Sunny Day: Flare Blitz, Lava Plume, Magma Storm
Swords Dance: X-Scissor
Worry Seed: Leech Seed
In case you didn't notice, DG has already added in the elemental fangs a few weeks/months ago.