A closure structured to adapt a syringe for connection to an incompatible standardized medical connector, including either a male or female ISO 80369 series ENFit® connector. An adapter body has an inlet port and an outlet port disposed in fluid communication with one another. The inlet port is dimensioned and configured to accommodate attachment to a discharge port of the syringe and the outlet port is dimensioned and configured to accommodate attachment to the standardized connector. A tip cap is removably connected to the adapter body in flow sealing relation to the outlet port. The closure may include a tamper evident assembly including a sleeve removably disposed in enclosing relation to the adapter body and tip cap and a retainer structure is disposed in removably retaining relation to the sleeve.