Impede the progress of (6)
(Other definitions for hamper that I've seen before include "Restrict, hinder" , "Food box; impede" , "Obstruct or delay with food basket" , "Prevent free movement" , "Stand in the way of the food basket" .)
(Other definitions for stymie that I've seen before include "Frustrate" , "Situation from which it is almost impossible to proceed" , "Prevent (by getting in the way)" , "Thwart -- my ties (anag)" , "Obstruct as on putting green" .)