Run a fiddle, taking a little off small cases of meat perhaps (7)
I believe the answer is:
ravioli
'small cases of meat perhaps' is the definition.
(ravioli may contain meat)
'run a fiddle taking a little off' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'fiddle' becomes 'violin' (synonyms).
'taking a little off' means to remove the last letter.
'violin' with its last letter removed is 'violi'.
'r'+'a'+'violi'='RAVIOLI'
(Other definitions for ravioli that I've seen before include "Filled form of pasta" , "you might have at La Scala?" , "Paganini might have made a meal of this" , "Pasta with savoury stuffing" , "Pasta resembling pillowcases" .)