Said to put the animal back outside (7)
I believe the answer is:
reputed
'said' is the definition.
(thesaurus)
'put the animal back outside' is the wordplay.
'the animal' becomes 'deer' (I've seen this before**).
'back' says the letters should be written backwards.
'outside' means one lot of letters goes inside another.
'deer' in reverse letter order is 'reed'.
'put' inserted into 'reed' is 'REPUTED'.
'to' acts as a link.
(Other definitions for reputed that I've seen before include "Generally believed to exist" , "Supposed" , "Generally believed (to be the case)" , "Deemed" , "Rumoured, reckoned" .)