Brigadier Karpov is the Officer in Charge of the TSC Army, and a member of the Starship Council. The equivalent US Army position and rank would likely be Army Chief of Staff and (four-star) General, respectively.
He is the founder of the Thunderfists, an elite special operations unit. He hand-picked the first class of this unit, ensuring that it would begin with the best of the best.
Karpov was Harkin's partner in the Enclave. He isn´t an expert in science, as shown by Dr. Nylus' jokes about Karpov thinking that he looks like a blue cat or has a pocket full of inventions, both clear references to Doraemon.