Kiss player possessing fine special quality (1,6)
I believe the answer is:
x factor
'special quality' is the definition.
(X factor can mean star quality)
'kiss player possessing fine' is the wordplay.
'kiss' becomes 'x' (X can represent a kiss).
'player' becomes 'actor' (synonyms).
'possessing' means one lot of letters goes inside another.
'fine' becomes 'f' (abbreviation).
'x'+'actor'='xactor'
'xactor' going around 'f' is 'X-FACTOR'.
(Other definitions for x factor that I've seen before include "'Hard to define but important special property (1,6)'" , "Popular TV talent show" , "Its judges hear appalling submissions" , "Indefinable special quality" , "Magical 'something'" .)