We present new near-infrared spectroscopic observations of the outer edges of the young stellar cluster around the supermassive black hole at the Galactic center. The observations show a break in the surface density profile of young stars at ∼13″ (0.52 pc). These observations spectroscopically confirm previous suggestions of a break based on photometry. Using Gemini Norths Near-Infrared Integral Field Spectrometer, we are able to detect and separate early- and late-type stars with a 75% completeness at Ks = 15.5.We sample a region with radii between 7″ and 23″ (0.28-0.92 pc) from Sgr A∗-and present new spectral classifications of 144 stars brighter than Ks = 15.5, where 140 stars are late-type (>1Gyr) and only four stars are early-type (young, 4-6Myr). A broken power-law fit of the early-type surface-density matches well with our data and previously published values. The projected surface-density of late-type stars is also measured and found to be consistent with previous results. We find that the observed early-type surface-density profile is inconsistent with the theory of young stars originating from a tightly bound infalling cluster, as no significant trail of young stars is found at radii above 13″. We also note that either a simple disk instability criterion or a cloud-cloud collision could explain the location of the outer edge, though we lack information to make conclusive remarks on either alternative. If this break in surface-density represents an edge to the young stellar cluster, it would set an important scale for the most recent episode of star formation at the Galactic center.