The ships schedule will be the same, muster at 4pm, sailaway 4.30pm, early dinner and first theatre show around 6pm, later dinner and second theatre show around 8pm.
The ship will be cleared to leave after muster but ports are like airports, the port authorities like air traffic control set the departure schedules. There could be multiple different reasons for a late departure. Dublin port for example is tidal, so the large cruise ships can only depart at high tide due to the depth of the harbour water. Sometimes the ship has a later departure due to space at the next port, or due to how busy the departure port is.