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 a hidden word.
'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" .)