Kay was promoted to Triple-A Syracuse on Monday, Anthony DiComo of MLB.com reports.
Kay will get his first taste of Triple-A after dominating across 12 starts for Double-A Binghamton, posting a 1.49 ERA, 0.92 WHIP and 70:23 K:BB in 66.1 innings of work. The 24-year-old southpaw still isn't on New York's 40-man roster, so he figures to finish out the season with Syracuse unless he really kicks the door down.