Greek character given Razzie upset in restaurant (8)
I believe the answer is:
pizzeria
'restaurant' is the definition.
(I've seen this before)
'greek character given razzie upset' is the wordplay.
'greek character' becomes 'pi' (letter from the Greek alphabet).
'given' says to put letters next to each other.
'upset' indicates an anagram.
'razzie' is an anagram of 'zzeria'.
'pi'+'zzeria'='PIZZERIA'
'in' acts as a link.
(Other definitions for pizzeria that I've seen before include "Italian-style restaurant" , "Restaurant serving Italian dishes of dough baked with savoury topping" , "Shop making and selling popular Italian food" , "Type of Italian restaurant" , "Kind of Italian restaurant" .)