Tapering stone pillar (7)
I believe the answer is:
obelisk
'tapering stone pillar' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for obelisk that I've seen before include "Needle-like column" , "Tapering, rectangular stone column" , "Ancient Egyptian monument" , "Tapering square stone monument" , "Cleopatra's Needle, perhaps?" .)