Put off animal with tempo (5)
I believe the answer is:
deter
'put off' is the definition.
(both can mean to discourage)
'animal with tempo' is the wordplay.
'animal' becomes 'deer' (deer is a type of animal).
'with' is an insertion indicator.
'tempo' becomes 't' (this might be a standard abbreviation which I don't know about).
'deer' going around 't' is 'DETER'.
Can you help me to learn more?
(Other definitions for deter that I've seen before include "Discourage through fear of consequences" , "Discourage or prevent from doing something" , "'Discourage, dissuade (5)'" , "Check" , "Prevent by instilling fear" .)