PKS 2023-07 is a flat spectrum radio quasar located at a redshift $z=1.388$, farther than any source currently detected at very high energies ($E>100$ GeV). At such energies, absorption by the extragalactic background light (EBL) renders the detection of distant sources particularly challenging. The High Energy Stereoscopic System (H.E.S.S.) observed the source following reports from AGILE (April 2016) and Fermi-LAT (April 2016, September and October 2017) on high flux states in gamma-rays. During each of the three flaring periods, near-simultaneous observations were obtained with H.E.S.S., Fermi-LAT and multiple telescopes at other wavelengths. Though the source was not significantly detected by H.E.S.S., upper limits were derived for each observation period. Through constraints given by Fermi-LAT in the MeV--GeV domain and upper limits by H.E.S.S., we searched for an intrinsic cutoff in the EBL-corrected gamma-ray spectrum of PKS 2023-07.