This is supposedly the grave of a general, Alcetas. From the Wikipedia: "To the south, west and north of the city, mostly within the city walls, there are large cemeteries containing rock-cut tombs, one is supposed to have belonged to Alcetas himself. Unfortunately the tomb has been despoiled by treasure hunters. In the tomb itself a kind of lattice work was carved between the columns behind the kline; at the top there was probably an ornamental frieze. The left part of the tomb is decorated with the depiction of a mounted warrior dateable to the 4th century BC. it is known that the youth of Termessos, much affected by the death of General Alcetas, built a magnificent tomb for him, and the historian Diodoros records that Alcetas did battle with Antigonos while mounted on a horse. These coincidences suggest that this is indeed the tomb of Alcetas and that it is he who is depicted in the relief."