Old Greek building new side, including this writer (10)
I believe the answer is:
archimedes
'old greek' is the definition.
'building new side including this writer' is the wordplay.
'building' becomes 'arch' ().
'new' indicates an anagram.
'including' indicates putting letters inside.
'this writer' becomes 'me' (the setter of the puzzle is the writer of the clue).
'side' is an anagram of 'ides'.
'ides' placed around 'me' is 'imedes'.
'arch'+'imedes'='ARCHIMEDES'
(Other definitions for archimedes that I've seen before include "Greek mathematician and inventor" , "'Eureka' scientist" , "Greek mathematician ('Eureka')" , "Old scientist" , "Ancient Greek mathematician/inventor" .)