A space command representative was a Starfleet officer who acted as a representative for Starfleet Command in certain court cases, including courts martial. These officers served as judges along with other appointed tribunal members, and held a rank of captain or higher.
In 2259, Zus Tlaggul was the space command representative in the case Starfleet v. Una Chin-Riley. (SNW: "Ad Astra per Aspera")
In 2267, Captain Lindstrom was the space command representative appointed by Commodore Stone in the case Starfleet v. James Kirk, held at Starbase 11. (TOS: "Court Martial")