Run in live game's first for scorer (4)
I believe the answer is:
berg
'scorer' is the definition.
(20th Century Austrian composer)
'run in live game's first' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'in' indicates putting letters inside.
'live game's first' becomes 'beg' (I can't explain this - if you can you should give a lot more credence to this answer).
'r' inserted into 'beg' is 'BERG'.
'for' acts as a link.
Can you help me to learn more?
(Other definitions for berg that I've seen before include "South African hill - Austrian composer" , "Mountain (in German, South African)" , "ice in the drink" , "African mount" , "Austrian composer of 12-tone music, d. 1935" .)