Crystal, electronic structure, dc and ac magnetization properties of the hole substituted (Sr2+) and partially B-site disordered double perovskite Pr2-xSrxCoMnO6 system have been investigated. The XRD pattern analysis showed a systematic decrease in the lattice parameters owing to the enhanced oxidation states of the Co/Mn ions. The electronic structure study by XPS measurements suggested the presence of mixed valence states of the B-site ions (Co2+ /Co3+ and Mn3+ /Mn4+) with significant enhancement of the average oxidation states due to hole doping. The mere absence of electronic states near the Fermi level in the valence band (VB) spectra for both pure (x = 0.0) and Sr doped (x = 0.5) systems indicated the insulating nature of the samples. Sr substitution is observed to increase the spectral weight near the Fermi level suggesting for an enhanced conductivity of the hole doped system. The dc magnetization data divulged a Griffiths like phase above the long-range ordering temperature. A typical re-entrant spin glass like phase driven by the inherent anti-site disorder (ASD) has been recognized by ac susceptibility study for both the pure and doped systems. Most interestingly, the emergence of a new cluster glass like phase (immediately below the magnetic ordering temperature and above the spin-glass transition temperature) solely driven by the Sr substitution has been unravelled by ac magnetization dynamics study. Observation of these dual glassy states in a single system is scarce and hence placed the present system amongst the rare materials. The isothermal magnetization measurements further probed the exhibition of the giant exchange bias effect originated from the interfacial exchange interactions due to existence of low temperature antiferromagnetic clusters embedded in the glassy matrix. © 2020 IOP Publishing Ltd.