If by "warp drive" you mean a drive that would be contracting spacetime in front of the ship and expanding it behind, then this ship wouldn't be subject to time

If by "warp drive" you mean a drive that would be contracting spacetime in front of the ship and expanding it behind, then this ship wouldn't be subject to time dilation. As it is not the ship that is exceeding the speed of light within a local reference frame (the "warp bubble) but the spacetime. But the feasibility of such a drive is purely understood at the moment as it seems such a drive would allow for causality violations.