Perhaps towards the end of the day, mean to eat with the Italian (8)
I believe the answer is:
twilight
'perhaps towards the end of the day' is the definition.
(period towards the end of the day)
'mean to eat with the italian' is the wordplay.
'mean' becomes 'tight' (synonyms).
'to eat' indicates putting letters inside.
'with' becomes 'w' (abbreviation).
'the italian' becomes 'il' ('the' in Italian).
'w'+'il'='wil'
'tight' going around 'wil' is 'TWILIGHT'.
(Other definitions for twilight that I've seen before include "Period of illumination when sun is just below horizon" , "Period just after sunset, becoming dark" , "Partial darkness" , "Period post-sunset" , "Declining stage" .)