  We present a study of the gas kinematics of star-forming galaxies associated
with protocluster 4C 23.56 at $z=2.49$ using $0''.4$ resolution CO (4-3) data
taken with ALMA. Eleven H$\alpha$ emitters (HAEs) are detected in CO (4-3),
including six HAEs that were previously detected in CO (3-2) at a coarser
angular resolution. The detections in both CO lines are broadly consistent in
the line widths and the redshifts, confirming both detections. With an increase
in the number of spectroscopic redshifts, we confirm that the protocluster is
composed of two merging groups with a total halo mass of $\log{(M_{\rm
cl}/M_{\odot})} =13.4-13.6$, suggesting that the protocluster would evolve into
a Virgo-like cluster ($>10^{14} M_{\odot}$). We compare the CO line widths and
the CO luminosities with galaxies in other (proto)clusters ($n_{\rm gal}=91$)
and general fields ($n_{\rm gal}=80$) from other studies. The 4C23.56
protocluster galaxies have CO line widths and luminosities comparable to other
protocluster galaxies on average. On the other hand, the CO line widths are on
average broader by $\approx50\%$ compared to field galaxies, while the median
CO luminosities are similar. The broader line widths can be attributed to both
effects of unresolved gas-rich mergers and/or compact gas distribution, which
is supported by our limited but decent angular resolution observations and the
size estimate of three galaxies. Based on these results, we argue that gas-rich
mergers may play a role in the retention of the specific angular momentum to a
value similar to that of field populations during cluster assembly, though we
need to verify this with a larger number of samples.
