Where is the ceremony weapon that unlocks a secret shrine?

The Ceremonial Trident is located underwater right by the northwest bridge, near where Trello tells you he dropped it in the lake. This video shows the location exactly.

Once you've found it, you can use a combination of Cryosis and Magnesis to fish the spear out of the water.

In addition to the ceremonial version of the weapon, that's location is discussed in MageXy's answer. You can also use the Lightscale Trident that you receive for completing divine beast vah Ruta to open the secret shrine.