Italian translation: normativa contrattuale applicabile
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leggi applicabili in materia di accordi, patti, convenzioni, contratti
Explanation: If you are translating from English to Italian the genus "agreement" under common law includes all the above.
If you text specifically refers to a "written" contract then you can probably safely abbreviate to "contratto".
Take a look a what "governing law" > " legge applicabile" your contract comes under and then decide.