We have obtained Keck spectra of six candidate globular clusters (GCs) in the dynamically young elliptical galaxy NGC 3610, supplementing our previous Keck spectra of eight confirmed GCs. Five of our new candidates are confirmed to be GCs. Of the 13 GCs, 11 are located within the K-band effective radius of 7 kpc. Two of these 13 clusters are found to be young (~2 Gyr) and very metal-rich ([Z/H]~+0.5), three are old and metal-poor, and the remaining eight clusters are old and metal-rich. The ages of the young clusters are consistent with a recent spectroscopic age estimate of 1.6+/-0.5 Gyr for the galaxy itself and suggest that these clusters formed in the disk-disk merger that likely created NGC 3610. Intriguingly, both young GCs have [α/Fe]~+0.3, while the majority of the old clusters are not α-enhanced, in contrast to Galactic and M31 GCs, and contrary to predictions of nucleosynthetic calculations. The two old subpopulations of GCs can be attributed to the merger progenitors. The relative numbers of old and new metal-rich GCs are poorly constrained because of the expected differences in radial distributions of the two subpopulations. However, based on our spectroscopic results and a comparison of the Hubble Space Telescope color-magnitude diagram with stellar population models, we argue that more than half of the metal-rich GCs are likely to be old.