I partially understand what you just said. So correct me if I'm wrong, I'll attempt to correct your terminology here.
1. You have a ContentField defined in a module.
2. You have a ContentPart defined in another module.
3. You defined a ContentType with ContentField and ContentPart added.
4. When you create a ContentItem, based on the ContentType definition, you want to trigger the ContentPartDriver after your ContentFieldDriver, because you have your logic split between them.
At this point, you should see that you're doing it wrong. Drivers should execute independently of one another. I suggest you change your abstractions.
Create one ContentPart with whatever fields you need doing everything that it needs to do.