You'll need some source of power, and some source of oxygen.
The O2 can be justified by some form of sealed fusion system turning water into helium and oxygen (Crack it for the H2, release the O2, fuse the H2 into He, Li, C and Be...). Or it could be by rock-eating semi-anaerobic bacteria (IE: Oxygen tolerant anaerobic strains), circulated by convection systems. Or it could be from the agricultural zone.
Water will be sealed cycle, unless you have a fusion plant.
Power could come from any number of sources, including geothermal, solar boilers, light conduits, radiothermal generators, sealed fusion or fission systems, bacterial battery stacks, or even Zero-Point Energy cells¹.
Water, food, and air are in fact going to be primarily functions of power distribution; if you can grow photosynthetic plants, you have food and air, plus recycling of organic wastes. The plants will give off water vapor, which can be drawn out and condensed elsewhere as pure water, and can be fed compost which has broken down the organic wastes of the animal load.
One way of getting light for those plants without electricity is the fiber-optic cable.... a thick (0.5m or even 1m) fiber cable cemented inside a conduit, leading from the surface down to growth chambers; the cable could be fed using mirrors, even, so the light is really bright.... such systems might even have redistribution nodes....
¹ ZPE cells are part of some theories behind Hawking Radiation and some other odd stuff. They are not generally accepted as plausible.