A casing? You mean a 'fairing' *psst* illegal.
A new seatpost would do it, but how do you get the right length for a user such that the hidden section is within the frame doesn't emerge and be beyond 3:1.
Given different thicknesses of handlebar tape, including gel inserts, don't count as fairings under UCI rules, I wonder if this would, given that it's making the seatpost less aero. Anyway, it maybe could be made an integral part etc etc. Even if not, it was a 10 second suggestion, so no need to be snarky.
As for my other suggestion, the hidden, non 3:1 section would be the same for every seatpost. The seatpost is inserted, and supported by the lip to the thicker section so it doesn't fall down further. Tighten seat post clamps as per usual to stop it lifting out. You would cut to length off the top, then insert the seat clamp fixture with some sort of attachment. The bit above the seat tube could effectively be the same dimension as the seat tube, and therefore legal.