Queen's Impatience
You must win a settlement before the Queen's Impatience rises too far or else you lose the city. Impatience slowly and gradually increases during your mission, starting from the moment after Embarking. Some modifiers make the rate of increase faster or slower, and some events can instantly subtract or add Impatience, potentially to its threshold and thus causing you to lose.
The red bar on the bottom right of the UI represents the time you have left to win. The bar fill red in the direction of the skull graphic. You can hover your mouse over the bar or the skull graphic to see a tooltip with the current value of the Queen's Impatience and the current rate at which Impatience is increasing. In this screenshot, taken at the beginning of a new city, the Queen's Impatience is 0 and increasing at a rate of 0.19 per minute. That means that, without any action, the run will end in about 73½ minutes. In reality, you could have much more time than this, and even after a long run many cities win with just a few points of Impatience due to subtractions.
Increases to the Queen's Impatience
The Queen's Impatience increases gradually. The rate depends on Citadel Upgrades you have purchased and current Perks in your settlement.
Impatience is also instantly added when Villagers leave or die, by 0.3. Therefore, if during a Storm three Villagers leave or die, when combined with the duration of the Storm, a full point would have been added to the Queen's Impatience in just a few minutes.
The Perk Mist Piercers increases Impatience by 0.5 for every newly opened Glade. (It may be worth it, however, since you will be able to see the contents of all Glades and can choose only the ones you need.)
Reductions to the Queen's Impatience
Whenever you finish an Order or complete a Glade Event that rewards Reputation, the amount of Reputation gained will be subtracted from the Queen's Impatience. Typically, the way you will see this is this: You will complete an Order that rewards 1.0 Reputation, and you will also be rewarded with a 1.0 reduction to Impatience.
When a Human is the Firekeeper in the Ancient Hearth, your settlement gets the Perk Beacon, which makes Impatience grow 25% slower. Therefore, if the rate of Impatience is +0.20 per minute, and you assign a Human to the Hearth, then the new rate of Impatience will be +0.15 per minute.