Was ist der Unterschied zwischen I'll draw up the contract. und I'll draw up a contract. ?Du kannst auch einfach Beispielsätze geben.

In real life, these two terms are used pretty much interchangeably. There's only a very slight difference in nuance but if this is just everyday speech I wouldn't even worry about it.

"I'll draw up THE contract"
This implies that the contract already exists or a format for the contract already exists. "The" is referring to one specific contract that you have in mind already.

Example:
A: "Here is my identification card."
B: "Great! Thank you. Now I'll get the contract from the back room. It'll just be a moment."

"I'll draw up A contract."
This implies that a contract is yet to be created or doesn't exist yet.

Example:

A: “Now that we have discussed the legality of everything, can you help me create a contact?"
B: “Sure. Once I draw up a contract for you everything will be good to go!"

Again the overall nuance is so small. I hope this helps! :)