Corset part to last (4)
I believe the answer is:
stay
I believe this clue is a double definition.
'corset part' is the first definition.
(I've seen this in another clue)
'last' is the second definition.
(I've seen this in another clue)
'to' acts as a link.
(Other definitions for stay that I've seen before include "Stanchion" , "Remain; suspend" , "Reside" , "Rope bracing a mast etc" , "Rope or wire used to support a mast" .)