Give up game after opponent captures rook (6)
I believe the answer is:
forego
'give up' is the definition.
'game after opponent captures rook' is the wordplay.
'game' becomes 'go' (go game is a kind of game).
'after' is a charade indicator (letters next to each other).
'opponent' becomes 'foe' (I've seen this before).
'captures' indicates putting letters inside.
'rook' becomes 'r' (abbreviation in chess).
'foe' going around 'r' is 'fore'.
'go' put after 'fore' is 'FOREGO'.
(Other definitions for forego that I've seen before include "Go without, give up" , "Go without (something desirable)" , "Get ahead" , "Precede (in place/time)" , "Go without (desirable thing)" .)