Put off animal, with time (5)
'put off' is the definition.
'animal with time' is the wordplay.
'animal' becomes 'deer' (I've seen this in other clues**).
'with' is an insertion indicator.
'time' becomes 't'.
'deer' enclosing 't' is 'DETER'.
(Other definitions for deter that I've seen before include "Inhibit", "Discourage (someone from an action)", "Discourage or prevent from doing something", "Discourage or impede", "Discourage through fear of consequences".)