Number clever enough for game show (7)
I believe the answer is:
tenable
'game show' is the definition.
(UK game show)
'number clever enough' is the wordplay.
'number' becomes 'ten' (ten is a kind of number**).
'clever enough' becomes 'able'.
'ten'+'able'='TENABLE'
'for' acts as a link.
(Other definitions for tenable that I've seen before include "Viable" , "Based on sound reasoning or evidence" , "Can be maintained" , "Believable" , "fairly arguable" .)