Meat, first portion of which is swallowed by dog (4)
I believe the answer is:
lamb
'meat first portion of which is swallowed by dog' is the definition.
'lamb' can be an answer for 'meat' (lamb is a kind of meat). I am not certain of the rest of the definition.
'which is swallowed by dog' is the wordplay.
'which' becomes 'm' (I can't explain this - if you can you should believe this answer much more).
'is swallowed by' indicates putting letters inside.
'dog' becomes 'lab' (short for labrador).
'm' going within 'lab' is 'LAMB'.
(Other definitions for lamb that I've seen before include "Charles ---, essayist; meek animal" , "Tender sheep meat" , "author?" , "Sweet and innocent child" , "Young farm animal" .)