Packing up the fight game? (6)
I believe the answer is:
boxing
'packing up' is the definition.
'boxing' can be an answer for 'packing' (I know this). I am unsure of the 'up' bit.
'fight game?' is the wordplay.
'fight' becomes 'box' (boxing is a kind of fighting).
'game?' becomes 'ing' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'box'+'ing'='BOXING'
'the' acts as a link.
Can you help me to learn more?
(Other definitions for boxing that I've seen before include "Fighting in a ring" , "The noble art?" , "Pugilist's sport" , "-- Day; -- glove" , "Combat sport" .)