Density dependence describes the regulation of population growth rate by population density. This process is widely observed in insect populations, including vectors such as mosquitoes and agricultural pests that are targets of genetic biocontrol using gene drive technologies. While there continues to be rapid advancement in gene drive molecular design, most studies prioritise gene drive efficacy over ecology, and the role of density-dependent feedback on gene drives remains neglected. Furthermore, the details of density dependence experienced in these potential species of interest are usually poorly understood, creating additional constraints and challenges in evaluating the efficacy and efficiency of gene drive systems, especially those that promise local confinement after release. Here, we formulate and analyse a simple, non-species-specific mathematical model which integrates population dynamics by density dependence together with population genetics of a high-threshold two-locus underdominance system. Different models of density dependence and strengths of within-species competition are investigated alongside other genetic and ecological parameters. Our results suggest that for an underdominance gene drive system, density dependence processes, by acting on births or deaths, influence the population dynamics by leading to significantly different population-level suppression in the presence of a fitness cost. However, density dependence does not directly affect the fitness cost threshold for drive establishment. Moreover, we find that the magnitude and range of key ecological parameters (birth and death rates) could result in different outcomes depending on the type of density dependence employed. Our work highlights the importance of considering the ecological contexts in the design, development and deployment of gene drive molecular strategies.