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The gamma beam system under construction at the ELI-NP facility in Romania is projected to give the nuclear physics community access to an experimental system providing a high-intensity, narrow bandwidth photon beam at variable energy. With high-efficiency detector systems in place, the experimental programme will have a strong potential for in-depth studies of rare stable isotopes originating from the astrophysical p-process. In particular, the neutron detection systems are already implemented through a dedicated 3He long neutron counter array, called ELIGANT-TN, that is completed and in use. In this mini-review, we will give a summary of the current status of existing (γ, n) cross-section data, as well as the methods to obtain them, and highlight the future potential to expand and improve such data using the ELI-NP instrumentation and beam-lines.