In this Letter, we investigate the threshold voltage (VTH) instability of Schottky p-GaN gate high electron mobility transistors (SP-HEMTs) under high-frequency operation by a resistive-load hard switching method. The abnormal VTH instability is observed, which is different between fully and partially depleted SP-HEMTs (FD- and PD-HEMTs). Notably, for FD-HEMT, VTH shifts positively with effective stress time. However, the VTH instability in PD-HEMT is more complex. At low VGS (e.g., 3 V) and high VGS (e.g., 6 V), VTH shifts positively with stress time consistently. Nevertheless, at intermediate VGS levels (e.g., 4 and 5 V), VTH initially shifts positively and then negatively, displaying a non-monotonous variation. Furthermore, the frequency dependence of VTH is contingent upon VGS. At low VGS, VTH exhibits a negative shift with the increase in frequency. This trend inverses when VGS exceeds 4 V. And it should be noted that the extracted VTH under high-frequency operation is lower than their quasi-static values for both transistor types. This work depicts the physical process and mechanism of the abnormal VTH instability; different from the quasi-static case, hole accumulation effects will be enhanced due to the high dV/dt, which results in a lower VTH. The distinct VTH behaviors of FD- and PD-HEMTs are closely related to the trapping effects, as well as hole accumulation and insufficiency, within the two different p-GaN gate layers.