They can be pursed or zipped (4)
I believe the answer is:
lips
(Other definitions for lips that I've seen before include "Edges of the mouth" , "Take, O take those - away (Measure for Measure)" , "Olivia's two, 'indifferent red' (T. Night)" , "Fleshy folds of tissue" , "Fleshy folds on the face" .)