We have a copy of the NEC3 Supply Contract, but there is nowhere for the parties to sign. Is there another document that sits with this, or do we have to create our own signing provisions?
The omission is quite deliberate. It is for the parties to decide how the contract is to be made because it could well depend upon the law of the contract (or even the law of the country one or more of the parties reside in). In the UK it could depend upon whether you want a deed, or not.
So you can make it as simple or as complicated as the applicable law requires. Simple offer and acceptance will do in the UK, or you can write out a more forma; document (deed or not) for both parties to sign.