Eccentric can't hope for monument (8)
I believe the answer is:
cenotaph
'for monument' is the definition.
(cenotaph is a kind of monument)
'eccentric can't hope' is the wordplay.
'eccentric' indicates an anagram.
'cant'+'hope'='canthope'
'canthope' is an anagram of 'CENOTAPH'.
(Other definitions for cenotaph that I've seen before include "War memorial" , "Monument honouring the fallen" , "Tomb-like monument to people buried elsewhere" , "Monument to those killed in war" , "Feature of Whitehall" .)