Star doesn't have time to eat fish (7)
I believe the answer is:
sardine
'fish' is the definition.
(sardine is a type of fish)
'star doesn't have time to eat' is the wordplay.
'doesn't have' indicates named letters should be taken away.
'time' becomes 't' (abbreviation).
'to eat' becomes 'dine' (to dine is to eat a meal).
'star' with 't' taken away is 'sar'.
'sar'+'dine'='SARDINE'
(Other definitions for sardine that I've seen before include "(Cramped?) fish" , "Fish (often tinned)" , "Rinsed a (anag) - fish" , "A diner's small fish" , "FRENCH FISH" .)