Hard to say what the next relic will be. The Vault of Glass was a raid centered around the concept of playing defensively, while Crota's End forced you to play offensively and the relics for each raid reflected this. Assuming that The Arena is a happy medium between offense and defense we may see a relic that is passive in nature, unlike the Aegis and Ascendant Sword.
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I would like to see some interesting buffs/debuffs to make the gameplay against a boss more interesting. You bring up some valid points. Maybe some armor that everyone picks up before going into the arena. Similar to the chalice of sorts.