I would definitely add the following clauses to your new contract:
- My free time is my time. I can code for others so long as there are no competitive issues, or sharing of code that I wrote for you.
- Code I write outside of working for you is mine. This is important due to the fact that some companies will add a clause that says, while under contract, all of your code is their intellectual property.
I would say this is pretty common practice and your current contract company should not care about this.
