We present the positions, proper motions, and near-infrared photometry for 966 known objects with spectral types later than M that were observed as part of the the UKIRT Hemisphere Survey (UHS). We augment the photometry and astrometry from UHS with information from Gaia DR3, Pan-STARRS DR2, and CatWISE 2020 to produce a database of homogeneous photometry and astrometry for this sample. The multi-epoch survey strategy of UHS allows us to determine the proper motions for most sources, with a median proper motion uncertainty of ~3.6mas/yr. Our UHS proper motion measurements are generally in good agreement with those from Gaia DR3, Pan-STARRS, and CatWISE 2020, with UHS proper motions typically more precise than those from CatWISE 2020 and Pan-STARRS but not Gaia DR3. We critically analyze the publicly available spectra for 406 members of this sample and provide updated near-infrared spectral types for ~100 objects. We determine typical colors as a function of spectral type and provide absolute magnitude versus spectral type relations for UHS J- and K-band photometry. Using newly determined proper motions, we highlight several objects of interest, such as objects with large tangential velocities, widely separated co-moving companions, and potential members of young nearby associations.