Four-sided tapering pillar (7)
I believe the answer is:
obelisk
'four-sided tapering pillar' is the definition.
(I've seen this before)
This is all the clue.
(Other definitions for obelisk that I've seen before include "Tapering square pillar" , "Tapering pillar erected as monument" , "Cleopatra's Needle, for instance" , "Pyramidal monument" , "Monument with four sides and tapering top" .)