Birds who could become slow (4)
I believe the answer is:
owls
'birds' is the definition.
(owl is a kind of bird)
'become slow' is the wordplay.
'become' is an anagram indicator.
'slow' is an anagram of 'OWLS'.
'who could' is the link.
(Other definitions for owls that I've seen before include "Slow sort of birds" , "Nocturnal bird" , "Strigiform creatures" , "Nocturnal hooters?" , "Slow (anag) -- birds of prey" .)