Happier somehow about start of Greek inscription (8)
I believe the answer is:
epigraph
'inscription' is the definition.
(epigraph is a kind of inscription)
'happier somehow about start of greek' is the wordplay.
'somehow' is an anagram indicator.
'about' means one lot of letters goes inside another.
'start of' suggests taking the first letters.
The initial letter of 'greek' is 'g'.
'happier' anagrammed gives 'epiraph'.
'epiraph' placed around 'g' is 'EPIGRAPH'.
(Other definitions for epigraph that I've seen before include "Quotation" , "Inscription (on building, coin, etc.)" , "Inscription on a building, statue or coin" , "Inscription on statue, coin, etc" , "Quote at start of book" .)