Monument not cheap to build (8)
I believe the answer is:
cenotaph
'monument' is the definition.
(I know that Cenotaph is a type of monument)
'not cheap to build' is the wordplay.
'to build' is an anagram indicator.
'not'+'cheap'='notcheap'
'notcheap' is an anagram of 'CENOTAPH'.
(Other definitions for cenotaph that I've seen before include "Whitehall memorial" , "Feature of Whitehall" , "Monument to those killed in war" , "War memorial" , "Monument built to honour soldiers who died in war" .)