Burke is a mortally wounded Starfleet chief whom Jake Sisko stumbles across on the battlefield of Ajilon Prime, and who dies after hearing Jake confess that he ran away.
Chief Burke appears in the fifth-season episode Nor the Battle to the Strong, played by Danny Goldring. He is a Starfleet soldier fighting the Klingons on Ajilon Prime who has been badly wounded while covering the withdrawal of his unit.
Jake Sisko finds him lying in the open after fleeing in panic from a bombardment that caught him and Julian Bashir on their way to a runabout. Jake tries to carry him to safety and, hoping for some kind of absolution, admits that he abandoned Bashir.
Burke gives him none. He tells Jake there is nothing to be done for him and dies where he lies, leaving Jake more ashamed than before. The encounter is the low point of Jake's experience of the war and shapes the article he writes afterwards.