Compton γ-ray sources have been used for over 30 years with new facilities being under construction or proposed. The gamma beam system under implementation at the Extreme Light Infrastructure - Nuclear Physics facility in Romania will deliver brilliant γ-ray beams with energies up to 19.5 MeV. Several instruments for measuring the parameters of the γ-ray beam are under development at ELI-NP. One of these instruments based on a High Purity Germanium detector is typically used for beam energy measurements at other facilities. Here we investigate the use of a High Purity Germanium detector to continuously monitor the intensity of the ELI-NP gamma beam by measuring the inelastic scattering of photons. This technique relies on both experimental and simulated data and it has been successfully tested during a recent experiment at the High Intensity γ-ray Source facility.