We report high-pressure Raman-scattering measurements on the transition-metal dichalcogenide (TMDC) compound HfS2. The aim of this work is twofold: (i) to investigate the high-pressure behavior of the zone-center optical phonon modes of HfS2 and experimentally determine the linear pressure coefficients and mode Grüneisen parameters of this material; (ii) to test the validity of different density functional theory (DFT) approaches in order to predict the lattice-dynamical properties of HfS2 under pressure. For this purpose, the experimental results are compared with the results of DFT calculations performed with different functionals, with and without Van der Waals (vdW) interaction. We find that DFT calculations within the generalized gradient approximation (GGA) properly describe the high-pressure lattice dynamics of HfS2 when vdW interactions are taken into account. In contrast, we show that DFT within the local density approximation (LDA), which is widely used to predict structural and vibrational properties at ambient conditions in 2D compounds, fails to reproduce the behavior of HfS2 under compression. Similar conclusions are reached in the case of MoS2. This suggests that large errors may be introduced if the compressibility and Grüneisen parameters of bulk TMDCs are calculated with bare DFT-LDA. Therefore, the validity of different approaches to calculate the structural and vibrational properties of bulk and few-layered vdW materials under compression should be carefully assessed.