Unknown female performer in the TV talent show (1,6)
I believe the answer is:
x factor
'the tv talent show' is the definition.
(I've seen this before)
'unknown female performer' is the wordplay.
'unknown' becomes 'x' (algebra).
'female' becomes 'f' (abbreviation).
'performer' becomes 'actor' (actor is a kind of performer).
'x'+'f'+'actor'='X-FACTOR'
'in' is the link.
(Other definitions for x factor that I've seen before include "Indefinable special quality" , "Noteworthy special quality" , "Magical 'something'" , "military hardship payment" , "Noteworthy special talent" .)