It was suggested to me by a friend that, provided no one dies and the vex do not take control of a sync plate, there would be a second chest that spawns once you raise the Spire & open the Vault. He showed me a path directly underneath the very first chest that takes you through a jumping puzzle to reach the Templar area. We didnt find anything whilst down there but there it is all the same.
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When facing the first chest, look to your right and you see the cliff immediately next to you. Now turn & face the chest & back off the edge slowly. This part can be completed by any of the three character types. I've done it with Hunters triple jump & with Warlocks glide. Just as you pass below the edge you dropped off of you will see an opening in the face of the cliff that you can get into. Once there you will find a full path that will take you a round about way to the Templar.