Unlike David, I only time block one day in advance, so if something comes up that needs to be done this week, but not today, I can just incorporate it when I time block a later day. If something comes up that needs to be done today, I’ll do it in lieu of one of the things I have scheduled. Sometimes I’ll cross the old item out and write the new one in (I do my time blocking on paper in a bullet journal) but often I won’t bother.
Speaking to a somewhat larger point, I see time blocking is a much more flexible system than what you’re describing. As I wrote in another thread:
For me, the key to making time blocking work is flexibility. I seldom have a day go precisely the way I planned it out. Stuff happens. Sometimes a task takes longer than anticipated. Sometimes something new pops up that needs to be done that day. Sometimes I find I can’t even get started on a task because I’m missing something critical.
When this happens, I just have to “roll with the punches” and adapt. I’ll push another task off until tomorrow, substitute a shorter task for a longer one, or drop something entirely. As @MacSparky put it, “A calendar is a soup rather than a puzzle.” Sometimes you have to stir the soup.