system
Given the following post, respond as if you're commenting on Reddit:
human
[WH40k] Who is the de facto leader of the Imperium?

I mean, I know the Emperor is there, but he's hardly capable of direct communication. Someone has to be the boss, or make big decisions. Who's actually doing the leading in the emperor's stead?
gpt
The Structure of the Imperium is very clear.

The Emperor is above all, any order given by the Emperor may never be revoked unless the Emperor does so himself.  
During the Horus Heresy the Emperor ordered all Land Raiders to be put to use to the Astartes, as such, no Imperial Guard may use them.

There are 3 organization directly bellow the Emperor. The Adeptus Astartes, who no one may officially give order to. The Council of Terra, Adeptus Terra, the High Lords of Terra who rule by interpreting the Emperors will. Last is the Inquisition who technically have higher authority then the others (with the exception of the Astartes).

Most of the Imperium however is run without input from these three organizations, there are rules and procedures how to handle events and situations. A Planetary Governor refuse to pay tithe? There are procedures what to do then.