The High Energy cosmic-Radiation Detection (HERD) facility has been proposed as one of several space astronomy payloads onboard the China Space Station (CSS). HERD will address several major problems in fundamental physics and astrophysics, including cosmic ray (CR) direct measurements up to PeV energies, dark matter searches, and a gamma-ray survey above 0.1 GeV. HERD consists of five sub-detectors, including a 3D imaging calorimeter (CALO) with two independent readout systems, based on image intensified CMOS (IsCMOS) camera and photodiodes (PD), respectively. The CALO is surrounded by a scintillating fiber tracker (FIT), a plastic scintillator detector (PSD) and a silicon charge detector (SCD). Additionally, a transition radiation detector (TRD) is placed on one of the lateral sides to provide accurate energy calibration. To accomplish the different HERD scientific goals, several trigger strategies have been defined. The baseline trigger relies on the energy deposited in different CALO regions and in the PSD. To enhance HERD science capabilities and calibration qualities, the advanced trigger strategy is designed with the information provided by the CALO PD, FIT and TRD. This will provide an efficient extension of the energy range for specific samples. The baseline and advanced trigger strategy will be presented, together with some optimization work of the calibration events selection in HE trigger channels.