Martin Kula began his career with the Memphis Police Department on June 5, 1989, as a Police Recruit at the Training Academy. Upon completion of basic training on October 20, 1989, he was assigned to Uniform Patrol at the West Precinct.

As a Police Officer, he worked various assignments which included West Precinct Charlie and Delta shift, South Precinct Charlie shift, Central Precinct Charlie shift, Wonders Charlie shift, Training Academy and General Assignment Bureau (GAB).

On July 12, 2000, Officer Kula was promoted to the rank of Sergeant. As a Sergeant, he was assigned to General Assignment BID.

On June 17, 2005, Sergeant Kula was promoted to the rank of Lieutenant. As a Lieutenant, he was assigned to Appling Farms Station Charlie shift, Crump Station Bravo shift and Crump Station GIB.

On October 14, 2016, Lieutenant Kula was promoted to the rank of Major. As a Major, he was assigned to Tillman Station Charlie shift and the Training Academy.

On February 18, 2023, Major Kula was appointed to the rank of Colonel. As a Colonel, he was assigned Executive Admin (Special Projects).

On January 4, 2025, Colonel Kula was appointed to Deputy Chief of Strategies and Special Projects.