Crisis at Hyrule Castle is the second quest you will get to do in the main storyline of The Legend of Zelda: Tears of the Kingdom.
The Crisis on hand? Hyrule Castle has levitated into the air. You need to find Princess Zelda somewhere in the earth below the floating castle and make sure she is safe.
Your first objective in all of this will be to find and speak with Captain Hoz who is leading a search party in Tears of the Kingdom.
Where to find Captain Hoz in Tears of the Kingdom
Finding Captain Hoz is not hard. He is located inside Hyrule Castle which you can reach by passing through the Hyrule Castle Town ruins. You will have a quest marker to follow so you will not get lost even if you try.
The only problem is getting to him. After your conversation with Purah, exit Lookout Landing and proceed north until you see the Castle Gates.
This is also when you will realize that you cannot enter the Castle, at least not through its gates, using your powers.
Get to the Gatehouse
You need to get to the gatehouse and to do so, look to the right of the gate. You will see a part of the wall has collapsed and you can jump over it. Do so and follow the path along the gate. Do take care not to fall.
You will then get to meet Raseno who confirms Captain Hoz’s location to be the Gatehouse. You must now head over there next by just following the road you are on.
Climb to the roof
Once you get to the gatehouse, the soldier present there will tell you Hoz is on the roof. The problem is, there’s no way to get to it that is obvious. There are two ways you can go about this, and both involve using your abilities. You will need Ultrahand and Ascend.
Get below the arch of the gatehouse and use Ascend to shoot through the air, pass through the arch and emerge on the other side. This is the easiest way to get there. But it requires you to have Ascend.
You can also choose to create a ramp by using Ultrahand to place the nearby wooden planks to form a bridge of sorts.
Using the same power, position it in such a way that it becomes a ramp and allows you to climb to the upper level. Then use Ultrahand again and pull it up and use it the rest of the way to get to the roof.
Once there, look for the soldier with a red feathered cap. That will be Captain Hoz; speak with him to mark your objective complete in Tears of the Kingdom.