Most relevant references either imply or state outright that Gil-galad passed the Red Ring to Círdan at the same time he passed the Blue Ring to Elrond (probably in II 1701, or at least soon after Sauron's expulsion from Eriador). The clearest example comes from Unfinished Tales Part Two, IV The History of Galadriel and Celeborn, where we're told, of the time immediately following Sauron's defeat: '...at this time Gil-galad gave Narya, the Red Ring, to Círdan Lord of the Havens...' On this basis Gil-galad would have been Guardian of the Ring for just eight years.
One account is entirely at odds with this narrative, however. From later in the same source, we're told that Gil-galad '...gave [the Ring] to Círdan when he set out from Lindon in the days of the Last Alliance'. If this is correct, then Gil-galad was Guardian of the Third Ring not for eight years, but for a total of no less than 1,738 years.