There is no single answer to this. Society itself is experimental and iterative. Each nation’s starting point for communism will be different, therefore administration of each communist experiment will be adapted to unique circumstances. Each nation’s development path of communism will be different, therefore each nation’s administration of that development will be different.

We do not yet know if all communist experiments will converge towards some shared administrative phenomena. There are plenty of people who have explored this in thought experiments, there are 6 communist experiments we can look to for real world lab results (China, USSR, Vietnam, Laos, DPRK, Cuba, am I forgetting one?), there are several other experiments we can look at (Paris Commune, Gotha Programme, Rojava, Zapatismo, others) but none of these could be considered the answer, just empirical evidence we can use to understand your question better and explore the set of possible answers, which is far larger than the experience we have so far.

That would be a society with such immense productive capacity and automation that it will change culture, education, and social relations so concepts like a police force may look significantly different (for example, the roles of a police force as we understand it now to be taken up by other sectors of society). Furthermore, given our growing understanding of epigenetics, microbiomes and medicine (as a discipline not just pharmaceutics), not withstanding bioengineering, the above quality of life improvements will likely change our biology as human beings as a whole.

This maybe a cop out answer but that is because we do not have the education yet of what a communist society will entail in the finer details; just a good scientific understanding how to get there. Heck, we haven’t even achieved global socialism yet. Quantitative changes will lead to changes of quality of society.