  We present NIRSpec IFS observations of a galaxy group around the massive
GS_4891 galaxy at z=3.7 in GOODS-South that includes two other two systems,
GS_4891_n to the north and GS_28356 to the east. These observations, obtained
as part of the GTO GA-NIFS program, allow for the first time to study the
spatially resolved properties of the interstellar medium (ISM) and ionized gas
kinematics of a galaxy at this redshift. Leveraging the wide wavelength range
spanned with the high-dispersion grating (with resolving power R=2700)
observations, covering from [OII]$\lambda$$\lambda$3726,29 to
[SII]$\lambda$$\lambda$6716,31, we explore the spatial distribution of
star-formation rate, nebular attenuation and gas metallicity, together with the
mechanisms responsible for the excitation of the ionized gas. GS_4891 presents
a clear gradient of gas metallicity (as traced by 12 + log(O/H)) by more than
0.2dex from the south-east (where a star-forming clump is identified) to the
north-west. The gas metallicity in the less-massive northern system, GS_4891_n,
is also higher by 0.2 dex than at the center of GS_4891, suggesting that
inflows of lower-metallicity gas might be favoured in higher-mass systems. The
kinematic analysis shows that GS_4891 presents velocity gradients in the
ionized gas consistent with rotation. The region between GS_4891 and GS_4891_n
does not present high gas turbulence which, together with the difference in gas
metallicities, suggests that these two systems might be in a pre-merger stage.
Finally, GS_4891 hosts an ionized outflow that extends out to r_out=1.2 kpc
from the nucleus and reaches maximum velocities v_out of approximately 400
km/s. Despite entraining an outflowing mass rate of M_out$\sim$2Msun/yr, the
low associated mass-loading factor, $\eta$=0.05, implies that the outflow does
not have a significant impact on the star-formation activity of the galaxy.
