Celeb has no time to eat fish (7)
I believe the answer is:
sardine
'fish' is the definition.
(I know this)
'celeb has no time to eat' is the wordplay.
'celeb' becomes 'star' (I've seen this in another clue).
'has no' 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' removed is 'sar'.
'sar'+'dine'='SARDINE'
(Other definitions for sardine that I've seen before include "Fish (often tinned)" , "Small fish, usually canned" , "Swimmer" , "Stonefish OR? Stone" , "(Cramped?) fish" .)