You can set contract notifications by going to Settings→ Configurations→ Scheduled Tasks→ Contracts.

Only the contract creator or administrator will receive an expiration notification for a specific contract.

If the contract has expired, the list table row will be filled with a red background.
You have the option of receiving contract expiration notifications additionally by email. Check the email template in Settings→ Email Templates.

If you do not want to receive contract expiration notification emails, simply deactivate this email template.