An executive department whose main funtion is to promote safety is

The Department of Justice.

Explanation:

The United States Department of Justice is a department of the Federal Government, headed by the United States Attorney General. This department is responsible for monitoring compliance with the law at the federal level, as well as guaranteeing administration of justice, with which it has a direct relationship with the federal Judiciary, headed by the Supreme Court. Today, the Attorney General of the United States is William Barr.

This department is in charge of monitoring compliance with the law at the federal level, with the ultimate objective of guaranteeing the safety and well-being in the lives of the nation's inhabitants. To do this, it has different subordinate agencies, such as the FBI and DEA, among others.