What you can do is explain to them that under that agreement, you will have to develop everything from scratch, and would be unable to use your existing extensive code already developed.
Ask them if they would like to save lots of money and time by licensing your existing code as well.
They may say that they want everything developed exclusively for them, in which case you will have to maintain completely separate code bases between your own stuff and what you (re)implement for them, and document the separation very carefully in logs.
Or sell them your existing code for a price if you are willing.
You just cannot have a situation in which you think you are only licensing them your code, and they think they are getting exclusive ownership of it. This is a recipe for disaster, even without a written contract. You need to discuss these issues with them and agree on a common view.
Ask them if they would like to save lots of money and time by licensing your existing code as well.
They may say that they want everything developed exclusively for them, in which case you will have to maintain completely separate code bases between your own stuff and what you (re)implement for them, and document the separation very carefully in logs.
Or sell them your existing code for a price if you are willing.
You just cannot have a situation in which you think you are only licensing them your code, and they think they are getting exclusive ownership of it. This is a recipe for disaster, even without a written contract. You need to discuss these issues with them and agree on a common view.