Two-dimensional topological insulators have attracted much interest due to their potential applications in spintronics and quantum computing. To access the exotic physical phenomena, a gate electric field is required to tune the Fermi level into the bulk band gap. Hexagonal boron nitride (h-BN) is a promising alternative gate dielectric due to its unique advantages such as flat and charge-free surface. Here we present a h-BN/graphite van der Waals heterostructure as a top gate on HgTe heterostructure-based Hall bar devices. We compare our results to devices with h-BN/Ti/Au and HfO2/Ti/Au gates. Devices with a h-BN/graphite gate show no charge carrier density shift compared to as-grown structures, in contrast to a significant n-type carrier density increase for HfO2/Ti/Au. We attribute this observation mainly to the comparable work function of HgTe and graphite. In addition, devices with h-BN gate dielectric show slightly higher electron mobility compared to HfO2-based devices. Our results demonstrate the compatibility between layered materials transfer and wet-etched structures and provide a strategy to solve the issue of significant shifts of the carrier density in gated HgTe heterostructures.