You can trade it for two things: Zonai Charges and Crystalized Charges. Zonai Charges are used in vending machines and to recharge your Energy Cell (personal battery) when you just need a little more juice to fly somewhere. Crystalized Charges are used to *upgrade * your Energy Cell so it lasts longer, but you do find a ton in the Depth in chests.

When using Autobuild, you don't actually need to have the required parts. Autobuild will manufacture the parts you need for 3 Zonaite each. In my opinion, that's the most important use for Zonaite Ore. At one point I had like 600 Zonaite Ore (regular size), and I actually ran out because I was using it so much for Autobuild.