Become engaged in game show (4)
I believe the answer is:
mesh
'become engaged' is the definition.
(to mesh is to interlink or become engaged)
'in game show' is the wordplay.
'in' says the answer is hidden in the clue.
'MESH' can be found hidden inside 'game show'.
(Other definitions for mesh that I've seen before include "Entangle, entwine" , "Engagement" , "Interconnected configuration" , "Get engaged" , "Knit or weave for Shem" .)