Elven tree gum appears in your game when you first reach sentient goods.
If you normal boosted good is steel, then tree gum will be your sentient boosted good.
You make it in a planks manufactury. You will need to build that planks manufactury right up to level twenty-something, you cant get tree gum from a little planks factory.
Alternatively you can buy tree gum in the trader, but you can only buy it with other sentient goods, not with normal goods. So you need to work out which is your boosted sentient, and start making that. Then you will be able to buy the others.
Or, as Gramps suggests, in the spire you can win "Gum Tree" buildings which will make a little gum for you.