After reaching the trench from the sand bowl elevator, you'll find the nornir chest in the alcove to the left side of the trench. To unlock it, you have to destroy three seals nearby. Cross the trench and operate the gear wheel to lower the platforms on both sides of the trench. Lower the platforms fully until you can’t turn the wheel anymore then freeze the smaller gear ahead to lock it in place. Turn around and you’ll find the first seal on a ledge behind you. Climb up and destroy it using a melee attack.
Recall the axe to lift the platform and give you access to the coffin above. Loot the Runic Forearm Bracers from it. Drop down to the gear wheel and operate it once more. Now, you don’t need to lower both platforms. Once the outer platform has been lowered, freeze the smaller gear. The seal is located in the other platform across the gear wheel, a little to the left of the smaller gear. Freeze the smaller gear and jump down the platform to destroy the rune.
Without recalling the axe, turn around to find the third seal in the other platform. After destroying it, recall your axe to lift the platforms again and loot the Idunn apple from it.
After restoring the light bridge, take the stairs to the left of the temple's front entrance. The nornir chest is found inside a tunnel blocked by a vine. There are two vine cores you have to destroy so move to the left so you have a direct line of sight for both. Throw your axe to destroy both of them and open the tunnel.
Once cleared, you have to ring the nearby bells in quick succession. The location of the three bells are quite obvious and placed near each other so they're hard to miss. Start of by ringing the bell near the stairs, then the one near the wall, and finally the last one above the nornir chest itself. Loot the Horn of Blood Mead inside.
After obtaining the Light of Alfheim and unlocking Atreus' Light Arrows, you'll eventually reach the temple's main entrance. Pick up the light crystal from the lore marker pedestal downstairs and insert it in the slot across the door.
Activate it to create a light floor above. Climb up the ledges nearby to reach the light floor. There’s a nornir chest behind and you’ll also get a good axe-throwing angle to take out the three small vine cores ahead as shown below.
After clearing that path, you can start finding the three bells needed to unlock the nornir chest. Get into position by the opening on the right side of the chest as shown below. This is where you’ll get a clear view of the bell outside the window.
After hitting it, hit the bell on top of the nornir chest, then press the down DPAD to quickly turn around where the last bell is located. This should unlock the chest containing a Horn of Blood Mead.
In the area with two gates that you can operate, follow the off-road path leading to a patio ruins with the chest. The bells you need to hit won’t display the symbols in them so you’ll have to hit the three correct bells in a short span of time to unlock the chest. Refer to the images of the correct bells below: