Not really, politics in ancient city-states revolved more around politicians increasing their own glory in competition with other aristocrats than implementing a shared programme/platform. When talking about Ancient Rome there were two political labels, optimates and populares, that are sometimes described as "parties" or (slightly m ore correctly) "factions" but this has been criticised by scholars for more than half a century now as explained by u/XenophonTheAthenian here, and discussed together with u/LegalAction in this older thread. For a more general discussion on Roman politics there is this answer by u/bigfridge224. Athens, with its more purely democratic system (Rome was a "mixed constitution") seems to have been even more alien to the idea of political parties, though an Ancient Greek historian would have to confirm that for me. At any rate u/Iphikrates has discussed at length how the Athenian political system functioned here.