  We show that the gravitational waves measurements have raised the opportunity
to measure $H_0$ with dark sirens to within 2$\sigma$, the accuracy required to
resolve the Hubble-Lema\^{i}tre tension. There are two principal reasons for
our results: (1) upgrades to GW LIGO-Virgo transient catalogues GWTC-1 and
GWTC-2 enhance their sensitive with only 10\% of contamination fraction, and
(2) new dark sirens should help to constrain our dynamical EoS. In conjunction,
sensitivity upgrades and a new dark energy model will facilitate an accurate
inference of the \hubble constant $H_0$ to better with an $\pm 0.007$ error in
comparison to the LIGO dark siren with $+14.0$/$-7.0$, which would further
solidify the role of dark sirens in late dark energy for precision cosmology in
the future.
