Some wag possibly inspiring hot TV programme (4,4)
I believe the answer is:
Here is my best explanation:
'tv programme' is the definition.
(I've seen this before)
'some wag possibly inspiring hot' is the subsidiary indication.
'possibly' indicates anagramming the letters.
'inspiring' means one lot of letters goes inside another.
'hot' becomes 'h'.
'somewag' is an anagram of 'gamesow'.
'gamesow' enclosing 'h' is 'gameshow'.
(Other definitions for game show that I've seen before include "Common TV format", "Genre of TV programme", "TV prize-winning programme" and "Competitive TV programme".)