Just as other ships may, submarines may also move out of a sea zone where they begin their turn with enemy ships, even destroyers. The destroyer doesn’t stop the sub’s movement, as the sub didn’t enter the sea zone - it started off there.
Yeah, didn’t see that thread was moved back until after I posted, but I thought I had seen mention of a UK bonus for controlling sea zones somewhere other than Lynxes’ post, such as one of the people that posted after seeing the game at Gen Con, I suppose I was mistaken though.