Predator not so much having one on (7)
I believe the answer is:
lioness
'predator' is the definition.
(I've seen this before)
'not so much having one on' is the wordplay.
'not so much' becomes 'less' (I've seen this in other clues).
'having' means one lot of letters goes inside another.
'one' becomes 'i' (Roman numeral).
'i'+'on'='ion'
'less' going around 'ion' is 'LIONESS'.
(Other definitions for lioness that I've seen before include "She may have pride" , "One with pride" , "Large cat" , "It's beastly" , "Female pride member" .)