Greek character visits second gravestone, possibly (8)
I believe the answer is:
monument
'gravestone possibly' is the definition.
(gravestone is a kind of monument)
'greek character visits second' is the wordplay.
'greek character' becomes 'nu' (Greek letter).
'visits' indicates putting letters inside (inserted letters visit the inside of another word).
'second' becomes 'moment' (synonyms).
'nu' inserted within 'moment' is 'MONUMENT'.
(Other definitions for monument that I've seen before include "Lasting record" , "Could be column" , "Memorial structure" , "cairn" , "London tube station" .)