A game for Henry to master (5)
I believe the answer is:
halma
'a game' is the definition.
(halma is a kind of game)
'henry to master' is the wordplay.
'henry' becomes 'hal'.
'to master' becomes 'ma'.
'hal'+'ma'='HALMA'
'for' acts as a link.
(Other definitions for halma that I've seen before include "played on board" , "Hopping board game" , "Leaping board game" , "Old board game" , "Board-game" .)