If the bad guy hears rumours about someone asking the question, does anything change?
When a clock fills in these contexts that should indicate that something needs to happen, and that something likely requires PC response. So if it isn't going to significantly impact the PCs until the third clock, it may as well be one big clock with stuff happening in the background as it fills. But if each clock has an impact and the PCs can do something to impact future clocks, stacking makes sense.
Regarding handling the consequence: it definitely depends. I'll sometimes use a clock if they're trying to overcome some major obstacle, so filling it means that they have less to deal with and that's probably going to be an RP exercise. But most of the time it's going to result in a change in position, or a need to resist something, or even a material change in their crew's territory that requires some response. In the example above, especially for such a large clock, I'd probably have the consequence be something like the bad guys invading their territory targeting the PC asking questions, which requires more than a mere change in position to resolve. That could involve a full-on heist to thwart.