A little puffin, is he drooled over? (8)
I believe the answer is:
finished
'over?' is the definition.
('finished' can be similar in meaning to 'over')
'a little puffin is he drooled' is the wordplay.
'a little' indicates a hidden word (a little bit of the clue).
'FINISHED' is hidden in the letters of 'puffin is he drooled'.
(Other definitions for finished that I've seen before include "dressed" , "exhausted" , "Complete" , "Brought to an end" , "Ended. completed" .)