A few years ago a ferry was brought in which sat in the new harbour waiting to sort out paperwork that never came through. That was intended to go to Gavdos.
Ask at Smerna Bar. There is a trip advertised on the small harbour but when we enquired, we were told that it needed something like 15 people (and calm weather I expect).
Turn up to Plakias in hope rather than expectation. Otherwise do as Hugo says and look at the main ferry timetable. Please report back if you manage the trip.