Round tripe pie not finished in ace eatery (9)
I believe the answer is:
trattoria
'eatery' is the definition.
(I know that trattoria is a type of eatery)
'round tripe pie not finished in ace' is the wordplay.
'round' shows that the letters should be reversed in order.
'tripe' becomes 'rot' (I've seen this in another clue).
'pie' becomes 'tart' (I've seen this before).
'not finished' means to remove the last letter.
'ace' becomes 'a' (abbreviation).
'rot'+'tart'='rottart'
'rottart' back-to-front is 'trattor'.
'in' with its last letter taken away is 'i'.
'trattor'+'i'+'a'='TRATTORIA'
(Other definitions for trattoria that I've seen before include "Italian restaurant" , "where Italians eat" , "Place to eat" , "Italian eating establishment" .)