Third of zoos with permits for young birds (6)
I believe the answer is:
owlets
'young birds' is the definition.
(young owls)
'third of zoos with permits' is the wordplay.
'third of zoos' becomes 'o' (3rd letter of 'zoos').
'with' becomes 'w' (abbreviation).
'permits' becomes 'lets' ('let' can be a synonym of 'permit').
'o'+'w'+'lets'='OWLETS'
'for' acts as a link.
(Other definitions for owlets that I've seen before include "Young wise birds" , "Baby wise old birds" .)