Activity of crook detective tails in a restaurant (6)
I believe the answer is:
scampi
'tails in a restaurant' is the definition.
(scampi is made from prawn or lobster tails)
'activity of crook detective' is the wordplay.
'activity of crook' becomes 'scam'.
'detective' becomes 'pi' (I've seen this in other clues).
'scam'+'pi'='SCAMPI'
(Other definitions for scampi that I've seen before include "Large sauteed prawns" , "sort of seafood" , "Fried seafood" , "Fish dish, often in rings" , "Dish of crustaceans" .)