How to address the important, but not urgent between Monday Hour One planning sessions?

Under the Monday Hour One scheduling system – how do you recommend keeping track of and ultimately schedule “to-dos” that are the results of daily actions? For example, you may be assigned a new project by your boss or accept a new client or your kids drink the last of the milk. Assuming that you are able to keep your originally pre-determined weekly schedule from Monday, what is the guidance for where to keep track of these until the next weekly planning session since we threw away the old to-do list after scheduling it on Monday?

Do you start a new list and add to it until the next planning session?

How to address the important, but not urgent?