Capitalize "Government Contract" when:
* It's a formal title: For example, you might say "The Government Contract for the new bridge project was awarded to XYZ Construction."
* It's a specific, named contract: If the contract has a name, like "The Government Contract for the National Defense Act," then capitalize it.
Don't capitalize "government contract" when:
* It's a general term: For example, "They are negotiating a government contract for the new software."
* It's part of a larger phrase: "The government contracts are overseen by the Federal Acquisition Regulation."
In doubt, err on the side of not capitalizing. You'll be more likely to be correct and the sentence will still make sense.