A science specialist was a specialist whose field of study was primarily focused on science.
In 2256, Captain Gabriel Lorca invited Michael Burnham to join the bridge crew of USS Discovery as a science specialist after Burnham had been previously stripped of rank following her court martial. (DIS: "Lethe")
In 2268, Spock objected to James T. Kirk piloting the shuttlecraft into the space amoeba because, among other things, he was not a science specialist. (TOS: "The Immunity Syndrome")