After you rescue Lefte and Wright from the rifts, the King and Link are still missing.

Visit Lueburry

Warp to Lueburry's house and go inside. There will be a cutscene.

From Lueburry's house, go north to reach Hyrule Field. Keep going north and go toward the quest destination. You will find a waypoint just south of a bridge. Check on it to add it to your map.

Go north up the bridge and there will be a cutscene.

Afterward, go north, and there will be another cutscene.

Help Hyrule Castle Town

You can optionally go counterclockwise around the outside of the town wall to find a Piece of Heart behind the northeast corner of the wall.

Then go into Hyrule Castle town and go northwest to where there is a well. Create an echo, such as an Old Bed, to reach the opening of the well. Jump down into it.

Go east and check on the glowing spot in the rift, then check on the opening to go in. You'll enter Stilled Hyrule Castle Town.