Well, it depends on the nature of this empire, it would probably need someone managing the empire's propaganda though.
You can also take inspiration from real-life ministers from governments, for example, realistically speaking, there should be someone focused on each major economical revenue of the empire, it can be mining, agriculture, alien-hunting, whatever.
Also, there should also be people managing development, education, everything that involves creating or maintaining the structures of the empire.
And at last, there should be people managing the legal power of the empire, such as its legal system, taxes, etc. And everything the empire has to maintain power, such as propaganda, as I have previously mentioned.
Hope it helped.