One killing animal — a small offence (8)
I believe the answer is:
assassin
'one killing' is the definition.
The answer is a person as well as being a singular noun. This is suggested by the definition.
'animal a small offence' is the wordplay.
'animal' becomes 'ass' (term for a donkey).
'small' becomes 's' (abbreviation - e.g. clothes size).
'offence' becomes 'sin' (a sin is an offence or transgression).
'ass'+'a'+'s'+'sin'='ASSASSIN'
Can you help me to learn more?
(Other definitions for assassin that I've seen before include "Political/religious killer" , "Killer of famous person" , "I kill" , "Killer of prominent person" , "Paid killer" .)