Game with prize — hard nut to crack? (8,4)
I believe the answer is:
treasure hunt
'game' is the definition.
(treasure hunt is a kind of game)
'prize hard nut to crack?' is the wordplay.
'prize' becomes 'treasure' ('treasure' can be a synonym of 'prize'**).
'hard' becomes 'h'.
'to crack?' indicates anagramming the letters (I've seen 'to crack' mean this).
'nut' with letters rearranged gives 'unt'.
'treasure'+'h'+'unt'='TREASURE HUNT'
'with' acts as a link.
(Other definitions for treasure hunt that I've seen before include "Solving clues for prize" , "Search conducted at children's birthday parties" , "Children's party game where things are sought" , "Game where players try to find things by following a series of clues" , "possible rally activity" .)