Migrant rook eggs picked up (5)
I believe the answer is:
rover
'migrant' is the definition.
(thesaurus)
'picked up' is the wordplay.
'picked' becomes 'r' (I can't justify this - if you can you should believe this answer much more).
'up' becomes 'over'.
'r'+'over'='ROVER'
'rook eggs' acts as a link.
This may not be right. Some or all of it may be part of another bit of the clue.
(Other definitions for rover that I've seen before include "Old scout" , "Pirate; dog's name" , "Wanderer, rolling stone" , "gypsy" , "Wanderer, archery mark" .)