A fundamental understanding of carrier transport is imperative for efficient semiconductor electronics and optoelectronics. Here, we use high speed black phosphorus photodetectors with sub-40 ps response time to elucidate carrier transport dynamics along its armchair and zigzag directions. Here we report a direct observation of carrier transport transition dynamics from phonon scattering transport to multiple trapping and release transport mechanism along the armchair direction, resulting from the relaxation of free carriers above the band edge to the band-tail states. We identified that the suppression of phonon scattering effects, a characteristic by Hall and field effect transistor measurements, is due to carrier transport in band tail states. Along the zigzag direction, only multiple trapping and release transport in band-tail states is observed, which might be due to low carrier mobility.