  We analysed a dedicated NuSTAR observation of the neutron-star low-mass X-ray
binary Z-source GX 13+1 to study the timing and spectral properties of the
source. From the colour-colour diagram, we conclude that during that
observation the source transitioned from the normal branch to the flaring
branch. We fitted the spectra of the source in each branch with a model
consisting of an accretion disc, a Comptonised blackbody, relativistic
reflection (relxillNS), and photo-ionised absorption (warmabs). Thanks to the
combination of the large effective area and good energy resolution of NuSTAR at
high energies, we found evidence of relativistic reflection in both the Fe K
line profile, and the Compton hump present in the 10--25 keV energy range. The
inner disc radius is $R_{\rm in} \lesssim 9.6~r_g$, which allowed us to further
constrain the magnetic field strength to $B \lesssim 1.8 \times 10^8$ G. We
also found evidence for the presence of a hot wind leading to photo-ionised
absorption of Fe and Ni, with a Ni overabundance of $\sim$6 times solar. From
the spectral fits, we find that the distance between the ionising source and
the slab of ionised absorbing material is $\sim 4-40 \times 10^5$ km. We also
found that the width of the boundary layer extends $\sim$3 km above the surface
of a neutron star, which yielded a neutron-star radius $R_{\rm NS}\lesssim 16$
km. The scenario inferred from the spectral modelling becomes self-consistent
only for high electron densities in the accretion disk, $n_e \sim
10^{22}-10^{23}$ cm$^{-3}$, as expected for a Shakura-Sunyaev disc, and
significantly above the densities provided by relxillNS models. These results
have implications for our understanding of the physical conditions in GX 13+1.
