Player with chips went up and down (4,4)
I believe the answer is:
deep blue
'player with chips' is the definition.
(chess playing computer - with microchips)
'went up and down' is the wordplay.
'went' becomes 'peed' (both can mean urinated).
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'and' is a charade indicator (letters next to each other).
'down' becomes 'blue' (I've seen this before).
'peed' backwards is 'deep'.
'deep'+'blue'='DEEP BLUE'
(Another definition for deep blue that I've seen is " Computer".)