Special quality has unknown element (1,6)
I believe the answer is:
x factor
'special quality' is the definition.
(I've seen this before)
'unknown element' is the wordplay.
'unknown' becomes 'x' (algebra).
'element' becomes 'factor' (synonyms).
'x'+'factor'='X-FACTOR'
'has' acts as a link.
(Other definitions for x factor that I've seen before include "'Hard to define but important special property (1,6)'" , "Its judges hear appalling submissions" , "Noteworthy special talent" , "military hardship payment" , "Indefinable special quality" .)