Game of skill caught old Nazi (5)
I believe the answer is:
chess
'game of skill' is the definition.
(I've seen this before)
'caught old nazi' is the wordplay.
'caught' becomes 'c' (cricket abbreviation).
'old nazi' becomes 'hess' (I've seen this before. I am not sure about the 'old' bit.).
'c'+'hess'='CHESS'
Can you help me to learn more?
(Other definitions for chess that I've seen before include "In which two bishops will participate" , "Musical - board game" , "show" , "Game with kings and queens" , "Sixteen-men-a-side game" .)