In Sukhothai you'll obtain 'Voss Note;, a collectible in his base that will point you towards there being three secret keys hidden across the game. One in the Vatican, one in Gizeh, and one in Shanghai. In this Indiana Jones and the Great Circle The Serpent's Chest Guide we'll go over how to find each of them, and what the reward is for gathering them all together.
By revisiting each of these locations you can obtain the secret keys
Vatican City Secret Key
Travel to the Dig Site in the South-East of the map, this is where the bulldozer fell into the tomb as part of the story. Once in the large tomb chamber head downstairs using the steps on the side and you'll reach the multistory chamber that you would have needed to stealth/beat up a number of Fascists when you first came through here.
Drop down and into the waterand in the far South-West of this room you'll be able to see a small hole in the wall. While in the water travel East and hop up onto the pillar that's just sticking out of the water. Run and jump onto the little ledge and then crawl into that hole to obtain the Vatican City Secret Key.
Gizeh Secret Key
Make your way to the Khentkawes Dig Site. Reach the Elevator down (you might have already fixed this) and follow the Blue power cable from the Elevator Switch until you reach the large room that is partially submerged in water.
To the right you'll see a flooded doorway, swim through here and immediately look for a log to move on your right. Move it and swim inside to obtain the Gizeh Key.
Shanghai Secret Key
The Shanghai key can be found at the very beginning of the Shanghai level, this sounds easy enough but unfortunately when you revisit this location you'll spawn into the end of the level.
From where you spawn in Shanghai backtrack through the level until you can jump into the water that leads you to the ground floor and the start of this area. Once you've reached the beginning of Shanghai jump in the water and travel around the corner to dislodge a log and get access to this Secret Key.
The Serpent's Chest Reward
Once you've obtained all three keys you need to return to the South-East most building in Voss' Camp in Sukhothai to open the chest.
Inside you'll find one of the Sukhothai Ancient Relics.