First of all, looking up, is greeting Italian — this one? (5)
I believe the answer is:
luigi
'this one?' is the definition.
The definition suggests a singular noun which matches the answer.
'first of all looking up is greeting italian' is the wordplay.
'first of all' says to take the initial letters.
The first letters of 'looking up is greeting italian' is 'LUIGI'.
(Other definitions for luigi that I've seen before include "Pirandello perhaps" , "- Pirandello, Italian author" , "-- Boccherini; -- Pirandello" .)