Buried heterostructure quantum cascade lasers (BH-QCLs) operating at high temperature in mid-infrared (MIR) to THz spectral range are desired for chemical sensing and free-space optical communication (FOC). In this work, Fe doped semi-insulating InP (SI-InP) regrowth is demonstrated in a hydride vapor phase epitaxy (HVPE) reactor for advanced MIR and THz BH-QCLs grown by MBE and MOCVD. SI-InP regrowth is implemented in THz QCL pillar arrays and narrow width and reverse-taper MIR BH-QCLs for efficient heat dissipation. By exploiting SI-InP regrowth, the parasitic capacitance in MIR distributed feedback BH-QCL can be suppressed, which is exploited for high speed FOC application.