Assuming that Cassiopeia has a right ascension of `approx ` 1hr (for example using `gamma ` Cas, the star in the center of the 'W'), then the sidereal time when Cassiopeia is on the meridian (taking the meridian to be the vernal equinox rather than a local meridian) is 1hr later than sidereal 'noon', which would be 1 'o' clock sidereal time.
This is because RA (right ascension) is the East-West coordinate of the constellation (or more specifically, a particular star within the constellation) at sidereal noon (when the vernal equinox has RA = 0hr). Since the stars rotate from East to West (or appear to, since we are spinning in the opposite direction), a star with RA 1hr to the right of the vernal equinox takes 1hr to ascend westward to the meridian.
However, usually, it is `beta ` Cassiopeia (or Caph), at the rightmost point of the 'W' that is used as a 'celestial clock' as it has RA `approx ` 0hr. When Cassiopeia is visible in the sky at night it is useful as a way of telling the time as it moves roughly 15 degrees every hour.