After returning from the Silent Realm, Fi will tell you that the Stone of Trials is one of a pair. The other one is in Skyloft. Go towards the waterfall to the northeast and cross the four rock platforms. On the other side, examine the bird statue with one eye and you’ll end up inserting the Stone of Trials beside what is apparently its partner.
Afterwards, the statue opens up, revealing a cannon. A cannonball is shot at the bottom part of the island with the Goddess Statue on it, and it soon crumbles to pieces. A structure beneath is revealed – it is your next dungeon, the Sky Keep. A few more cannonballs are shot, which become Clawshot targets.
After the scene, stock up at the Bazaar if you feel like it, then cross the Clawshot targets and go into the structure.