Eat like a bird (7)
I believe this is a double definition.
'eat' is the first definition.
(I've seen this before)
'bird' is the second definition.
(swallow is a kind of bird)
'like a' acts as a link.
(Other definitions for swallow that I've seen before include "Take in - migratory bird" , "Accept" , "Migrating bird" , "Small migratory bird with forked tail" , "Creature which can go up" .)
'eat like a bird' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for peck that I've seen before include "Gregory" , "Bite lightly; a dry measure" , "Attack with beak" , "Kiss; old dry measure" , "Kiss; part of bushel" .)