Terry Burrell is an officer in the Colonial Fleet Marine Corps.
He is on board the Rising Star on leave when Sesha Abinell and her group take their hostages. He's also part of a failed rescue attempt which results in him getting shot in the leg, two dead Marines, and one dead hostage-taker. (Sacrifice)
Notes
There is some confusion over his rank. Starbuck refers to him as 'Gunny', suggesting he is a Gunnery Sergeant, but the closing credits of Sacrifice list him as 'Lt. Terry Burrell', which makes the 'Gunny' comment very confusing. At this time, we should consider him a Lieutenant, since that's the rank the credits list him as, with the 'Gunny' comment being a reference to a recent promotion from Gunnery Sergeant to lieutenant.