Pledged to have shelf (5)
I believe the answer is:
ledge
'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' can be found hidden inside 'pledged'.
(Other definitions for ledge that I've seen before include "Sill" , "Mantelpiece" , "Shelf-life projection" , "Ridge or shelf" , "Projecting ridge on a mountain" .)