There are at least three bands called Discovery.
1) Discovery is a collaboration of Ra Ra Riot’s Wes Miles and Vampire Weekend’s Rostam Batmanglij. Some of the songs are sung by Wes, some are sung by Rostam, and some are sung by the two of them together. Their first album, appropriately and simply dubbed "LP" came out on XL on the 7th of July 2009.
2) Discovery is a funk/prog pop duo from Brooklyn, NY, that released an LP in 2010 and has been featured in many major NYC music publications.