After fault, catch up for game (6)
I believe the answer is:
tennis
'game' is the definition.
(tennis is a kind of game)
'after fault catch up' is the wordplay.
'after' says to put letters next to each other.
'fault' becomes 'sin' (I've seen this in other clues).
'catch' becomes 'net' (netting is a kind of catching).
'up' is a reversal indicator (in down clue: letters go upwards).
'sin' next to 'net' is 'sinnet'.
'sinnet' in reverse letter order is 'TENNIS'.
'for' is the link.
(Other definitions for tennis that I've seen before include "Racquet-game" , "Real or lawn game" , "Sent in, strangely, for sport" , "Henman's game" , "Medieval, originally French, sport, codified by the British" .)