Pledged to have a shelf (5)
I believe the answer is:
ledge
'a shelf' is the definition.
(I know that shelf can be written as ledge)
'pledged to have' is the wordplay.
'to have' indicates the answer is hidden within the clue.
'LEDGE' is hidden within 'pledged'.
(Other definitions for ledge that I've seen before include "Shelf-like projection" , "Narrow projecting shelf as from window" , "Narrow projection or shelf" , "Projecting shelf, horizontal projection" , "Mantelpiece" .)