Column but not newspaper’s cover (7)
I believe the answer is:
plaster
'cover' is the definition.
(plastering is a kind of covering)
'column but not newspaper's' is the wordplay.
'column' becomes 'pilaster' (pilaster is a kind of column).
'but not' indicates named letters should be taken away.
'newspaper' becomes 'i' (UK newspaper).
'pilaster' with 'i' taken away is 'PLASTER'.
(Other definitions for plaster that I've seen before include "Medical dressing" , "Render (walls)" , "Strip of material for dressing wound" , "One to cover wall, wound" , "Wall/ceiling covering" .)