  We compute the exclusive photoproduction of a $\gamma\,\pi^\pm$ pair using
the collinear factorisation framework, in the kinematic regime where the pair
has a large invariant mass. This exclusive channel presents a new avenue for
the investigation of GPDs. It is particularly interesting as the high centre of
mass energies available at future experiments will allow the study of GPDs at
small skewness $ \xi $. We compute the scattering amplitude of the process, at
leading twist and leading order in $\alpha_s$, which is used to estimate its
cross-section and linear polarisation asymmetries with respect to the incoming
photon, for JLab~12-GeV, COMPASS, future EIC and LHC (in ultra-peripheral
collisions) kinematics. We find that the order of magnitude of estimates are
sufficiently large for a dedicated experimental analysis to be performed,
especially at JLab. We also compare the results from an asymptotic distribution
amplitude (DA) to those using a recently proposed \textit{holographic} DA.
