  We present results from MUSE observations of a 21-cm HI absorption system
detected with the Australian Square Kilometre Array Pathfinder radio telescope
at redshift $z = 0.4503$ towards the $z = 1.71$ quasar PKS 1610-771. We
identify four galaxies (A, B, X and Y) at the same redshift as the 21-cm H I
Damped Lyman-{\alpha} (DLA) absorption system, with impact parameters ranging
from less than 10 kpc to almost 200 kpc from the quasar sightline. Ca II and Na
I absorption is seen in the MUSE spectrum of the background QSO, with
velocities coinciding with the initial HI 21-cm detection, but tracing less
dense and warmer gas. This metal-line component aligns with the rotating
ionised disc of galaxy B (impact parameter 18 kpc from the QSO) and appears to
be co-rotating with the galaxy disc. In contrast, the 21-cm HI absorber is
blueshifted relative to the galaxies nearest the absorber and has the opposite
sign to the velocity field of galaxy B. Since galaxies A and B are separated by
only 17 kpc on the sky and $70$ km s$^{-1}$ in velocity, it appears likely that
the 21-cm detection traces extragalactic clouds of gas formed from their
interaction. This system reveals that the cold 100 K neutral gas critical for
star formation can be associated with complex structures beyond the galaxy
disc, and is a first case study made in preparation for future large 21-cm
absorption surveys like the ASKAP First Large Absorption Survey in HI.
