How are you going to feed the sub panel if there are no spaces left in the panel? Are you going to move two of the existing circuits into your new panel? I have never seen a 240V hot tub designed to be connected with a cord so make sure that this is not something that was added by a former owner of the tub. In my area the only tubs that come with cords are the 20A 120V models and all of the 240V units are designed to be hard wired. Also remember if this receptacle is installed in a wet location it must have a cover approved for wet locations while in use. I am not sure how available these are for 50A receptacles.
