Feel free to downvote because I don't really know if this is *that* untranslateable, but I always find myself grasping for this word in both German and English. Whereas "government" often refers to a specific administration, like the "Blair government", especially in European contexts, overheid differentiates from the Dutch "regering" because it generally doesn't refer to the legislature or executive and much more to government bureaucracy. You would pay your taxes to the overheid, but the overheid doesn't decide what to do with your taxes, it only spends them.
Wouldn’t this simply be government in English? What nuance does “overheid” have that “government” does not?
Overheid means government. Nothing more.
“Bureaucracy” seems to be a sensible English translation.