Not a contemptible person, flipping cross (5)
I believe the answer is:
tigon
'cross' is the definition.
(offspring of a lion and a tiger)
'not a contemptible person flipping' is the wordplay.
'not' becomes 'no' (negative).
'a contemptible person' becomes 'git' (git can mean an annoying person).
'flipping' says the letters should be written in reverse.
'no'+'git'='nogit'
'nogit' back-to-front is 'TIGON'.
(Other definitions for tigon that I've seen before include "Hybrid offspring of two big cats" , "Animal" , "Tiger-lion hybrid" , "Cross between two big cats" , "Cross between tiger and lion" .)