Famous writer's sporting run (5)
I believe the answer is:
homer
'famous writer's' is the definition.
'homer' can be an answer for 'writer's' (Homer is an example). I am not sure about the 'famous' bit.
'sporting run' is the wordplay.
'sporting' becomes 'home' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'run' becomes 'r' (cricket abbreviation).
'home'+'r'='HOMER'
Can you help me to learn more?
(Other definitions for homer that I've seen before include "addition to the score?" , "linesman" , "Ancient Greek author" , "Greek poet - TV's Simpson" , "pigeon, maybe" .)