Dungeoneer's Pack

Only one player can have the initiative at a time. As one player takes the initiative, any other player that had the initiative ceases to have it.

If you're already in a dungeon when instructed to venture into Undercity, you move to the next room of that dungeon. If you are already in the last room, you will complete that dungeon and start Undercity. This is true whether you're already in Undercity or any other dungeon.

You cannot venture into Undercity unless instructed to do so, either because you have the initiative at the beginning of your upkeep or because you take the initiative. Notably, if you aren't in a dungeon and an effect instructs you to venture into the dungeon (not venture into Undercity), you can't start Undercity.