In this work, the gate current characteristics are investigated to explain the threshold voltage shift in AlGaN/GaN high electron mobility transistors (HEMTs) with a p-GaN gate. First, the intrinsic gate current conduction mechanisms are identified: in the low bias range (2.5 V $ < {V}_{G} < $ 4 V), thermionic emission (TE) dominates in the AlGaN/GaN region, whereas in a higher bias range (4 V $ < {V}_{G} < $ 7 V) trap-assisted tunneling (TAT) is occurring in the Schottky/p-GaN region. Secondly, the threshold voltage shift of the stress phase is evaluated by applying a positive gate bias for various stress times. A consistent trap level with an activation energy of ${E}_{A}\sim $ 0.6 eV is found. In conclusion, a physical model explaining the negative ${V}_{\text {TH}}$ shift by considering TAT via hole transport is proposed.