This level is a swine to put it mildly. Check it out with True Seeing and you'll see a checkerboard of yellow. The place is riddled with spinners and trapdoors. All the trapdoors lead to Level 5, the Lava Cellar, and I got sick to the back teeth of dropping down to there, trudging back, being spun and then falling through another trapdoor. To be brief, they are just a pain and a time waster.
Two bits of info from NPCs. One tells you that the elemental bound by the wizard is En-Li-Kil and he commands time itself. Another says that in the King's Domicile is an elevator that will take you to Cleowyn's Palace. King Cleowyn used to use it to bypass the traps around his throne. (That is through the door at B2 which is opened using the Domicile Key. What? You haven't got that yet? Okay, I'll tell you where it is, you fight for it at C14).
Stairs lead to the Level 3 Great Corridor at P16 and there's a teleport to the Level 1 Vestibule at A1. You arrive from Cleowyn's Palace via the pit there to B1 and the elevator is at C1. A blue lockpick opens most locked doors here. There are many square rooms arranged regularly around this area. Some have one way doors which can be a bind as they force you to drop through a trapdoor when you leave.
The central room contains two teleports. One from the Level 3 Great Corridor is at H8 and one on the opposite side of the room, I9, leads to the Lava Cellar on Level 5. This is the way you will return after falling through a trapdoor. To leave this room and enter the area proper, cast Detect facing the south wall at H9 and you'll find a secret door. Stairs to Level 5, the Thieves' Den, go down from C8.
One NPC at N16 tells you that this is the lowest level of Cleowyn's Palace but merely the beginning of the dungeon proper. We still have a long way to go ...