We present near-IR (1.0Y2.5 m) photometry and spectroscopy of HD 3651B, the low-luminosity, wide-separation (480 AU ) companion to the K0 V exoplanet host star HD 3651A. We measure a spectral type of T7.5AE0.5 for HD 3651B, confirming both its substellar nature and the fact that wide-separation brown dwarfs and giant planets can coexist around the same star. We estimate an age of 3Y12 Gyr for the primary star HD 3651A and find that it is %3 times older than the K4 V star Gl 570A (%1Y5 Gyr), the host star of the T7.5 dwarf Gl 570D. We derive a bolometric luminosity of log (L bol /L ) ¼ À5:58 AE 0:05 for HD 3651B and infer an effective temperature of 780Y840 K and a mass of 40Y72 M Jup ; the luminosity and temperature are among the lowest measured for any brown dwarf. Furthermore, HD 3651B belongs to the rare class of substellar objects that are companions to main-sequence stars and thus provides a new benchmark for studying very low temperature objects. Given their similar temperatures (ÁT eA % 30 K ) and metallicities (Á½Fe/H % 0:1 dex) but different ages, a comparison of HD 3651B and Gl 570D allows us to examine gravity-sensitive diagnostics in ultracool spectra. We find that the expected signature of HD 3651B's higher surface gravity due to its older age, namely a suppressed K-band flux relative to Gl 570D, is not seen. Instead, the K-band flux of HD 3651B is enhanced compared to Gl 570D, indicative of a younger age. Thus, the relative ages derived from interpretation of the T dwarf spectra and from stellar activity indicators appear to be in discord. One likely explanation is that the K-band fluxes are also very sensitive to metallicity differences. Metallicity variations may be as important as surface gravity variations in causing spectral differences among field late-T dwarfs.