Optimism regarding potential epidemiological and conservation applications of modern gene drives is tempered by concern about the possibility of unintended spread of engineered organisms beyond the target population. In response, several novel gene drive approaches have been proposed that can, under certain conditions, locally alter characteristics of a population. One challenge for these gene drives is the difficulty of achieving high levels of localized population suppression without very large releases in the face of gene flow. We present a new gene drive system, Tethered Homing (TH), with improved capacity for both localization and population suppression. The TH drive is based on driving a payload gene using a homing construct that is anchored to a spatially restricted gene drive. We use a proof-of-concept mathematical model to show the dynamics of a TH drive that uses engineered underdominance as an anchor. This system is composed of a split homing drive and a two-locus engineered underdominance drive linked to one part of the split drive (the Cas endonuclease). We use simple population genetic simulations to show that the tethered homing technique can offer improved localized spread of costly transgenic payload genes. Additionally, the TH system offers the ability to gradually adjust the genetic load in a population after the initial alteration, with minimal additional release effort. We discuss potential solutions for improving localization and the feasibility of creating TH drive systems. Further research with models that include additional biological details will be needed to better understand how TH drives would behave in natural populations, but the preliminary results shown here suggest that tethered homing drives can be a useful addition to the repertoire of localized gene drives.