The nature and stability of the disordered phase I and the ordered phase III of solid hydrogen bromide under pressure were investigated using the ab initio molecular dynamics method. A detailed study of the response to pressure of the orientational distribution and the orientational and vibrational dynamics in disordered phase showed that phase I can be described as a rotator phase with fluctuating hydrogen bonds up to pressures well over 10 GPa. We predict that the disorder at higher densities leads to cooperative proton-transfer dynamics. The pressure dependence of stretching modes in phase I and lattice modes in phase III was also investigated and compared well with experimental data.