To use the new buildings, modules, and edict, you will need to research them. There are 4 techs you can research in total, each granting you 5 free admin cap points, as well as unlocking buildings etc. The techs will become available from the RNG in the society branch.

The first Tier: "Infrastructure Analytics" - should become available pretty early in the game, with a greater chance of appearance should you have a scientist with the skill "New Worlds", which is indicated by a green flag icon. Once you unlock it, you will get 5 free admin capacity, and the ability to build the first tier admin office buildings on your worlds. (one for each world only) - each granting you 4 additional capacity, and adding clerk and research jobs. Gestalt will get maintenance drone and calculator drone jobs. You will also be able to build the starbase modules which add 2 capacity.

The second tier "National Expansion Administration" - will appear after you research the first tier, with a greater chance of appearing if you have a scientist in the society slot with the "New Worlds" skill. Unlock this one for an additional 5 free admin capacity, and grant you access to an upgrade for each of your buildings which gives +16 admin capacity each as opposed to 4.

The third tier, "National Expansion Administration" - will appear after you research the second tier, with a grater chance of appearing if you have a scientist in the society slot with the "Statesman" skill, indicative of an icon with shaking hands. Unlock this to get access to building upgrades that give you +32 admin cap each, as opposed to +16.

The final tier, "Galactic Expansion Operations" - is rare and might be challenging to appear, there is no scientist skill that increases its chances. Once you unlock it, your buildings can now grant +64 admin capacity each, should you upgrade them of course. You will also get access to a powerful "Galactic Census" edict which will cut any of your negative sprawl effects by 50%, use this if you are over capacity and want an edge for 10 years or so to either catch up or research new tech.