  Investigating the Gunn-Peterson trough of high redshift quasars (QSOs) is a
powerful way to reveal the cosmic reionization. As one of such attempts, we
perform a series of analyses to examine the absorption lines observed with one
of the highest redshift QSOs, PSO J006.1240+39.2219, which we previously
discovered at z = 6.62. Using the Subaru telescope, we obtained
medium-resolution spectrum with a total exposure time of 7.5 hours. We
calculate the Ly$\alpha$ transmission in different redshift bins to determine
the near zone radius and the optical depth at 5.6$<$z$<$6.5. We find a sudden
change in the Ly$\alpha$ transmission at 5.75$<$z$<$5.86, which is consistent
with the result from the literature. The near zone radius of the QSO is
5.79$\pm$0.09 $p$Mpc, within the scatter of the near zone radii of other QSOs
measured in previous studies. We also analyze the dark gap distribution to
probe the neutral hydrogen fractions beyond the saturation limit of the
Gunn-Peterson trough. We extend the measurement of the dark gaps to
5.7$<$z$<$6.3. We find that the gap widths increase with increasing redshifts,
suggesting more neutral Universe at higher redshifts. However, these
measurements strongly depend on the continuum modeling. As a continuum
model-free attempt, we also perform the dark-pixel counting analysis, to find
the upper limit of $\langle x_{\rm H I} \rangle \sim$0.6 (0.8) at $z<$5.8
($z>$5.8). All three analyses based on this QSO show increasingly neutral
hydrogen towards higher redshifts, adding precious measurements up to
z$\sim$6.5.
