Animal at all times allowed out (7)
I believe the answer is:
leveret
'animal' is the definition.
(I've seen this before)
'at all times allowed out' is the wordplay.
'at all times' becomes 'ever' ('ever' can be a synonym of 'at all times').
'allowed' becomes 'let' (I've seen this before).
'out' means one lot of letters goes inside another.
'ever' inserted within 'let' is 'LEVERET'.
(Other definitions for leveret that I've seen before include "youngster in form" , "Young three dn" , "Speedy young thing" , "Hare in its first year" , "Small hopper" .)