To enforce compliance with tagging policies in real-time:

AWS Config Setup: Implement an AWS Config rule to continuously monitor and evaluate EC2 instances for compliance with the tagging requirements. The required-tags managed rule can be configured to specifically check for the presence of a 'department' tag.

Automatic Remediation: Configure AWS Config to automatically execute the AWS-TerminateEC2Instance Systems Manager Automation document as a remediation action. This runbook will terminate any EC2 instance identified as noncompliant due to missing required tags.

Operational Efficiency: This setup allows for the enforcement of company tagging policies automatically and in near real-time, reducing the manual overhead of monitoring and ensuring compliance.

This method provides an efficient and effective solution to ensure that all EC2 instances meet the company's tagging requirements and that any noncompliant instances are dealt with promptly.