Clue: Spoil a pet badly, fed with last of supper – source of nasty bacteria (10)
Answer: LEPTOSPIRA
Explanation: Spoil a pet badly, fed with last of supper – source of nasty bacteria (10)
***(spoil a pet)** *fed with [last of]* (suppe)**R** 
*Leptospira is a genus of bacteria, an infection of which can cause some nasty side-effects.