Diana's game show (7)
I believe the answer is:
'show' is the definition.
(display can mean to show or expose)
'diana's game' is the wordplay.
'diana' becomes 'Di' (Di is short for Diana).
'game' becomes 'splay' (I can't justify this - if you can you should give a lot more credence to this answer).
Can you help me to learn more?
(Other definitions for display that I've seen before include "Exhibition" , "Showcase" , "Put on show" , "Demonstrate, show" , "Show to the public" .)